Latex alternatives

Author: c | 2025-04-25

LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX.

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Bakoma TeX is a TeX-based typesetting system tailored for Microsoft Windows, designed to simplify the process of document creation using TeX/LaTeX. With a user-friendly interface, it allows users, whether they are seasoned professionals or new to the field, to efficiently compile complex documents that require advanced typographical features. Bakoma TeX incorporates an intuitive editor and various tools that enhance productivity and make working with TeX styles, fonts, and layouts more accessible. Here are some software products that are alternatives or complement Bakoma TeX for typesetting and document preparation using TeX or LaTeX languages. These products cater to a range of user needs from simple text editing to complex document management. In addition to the aforementioned products, there are other software alternatives that provide similar functionalities for handling documents in TeX and LaTeX. These alternatives might cater to specific use cases or preferences in user experience. Related searches » bakoma tex кряк » bakoma tex download » bakoma tex trial лечилка » bakoma tex лекарство » bakoma tex serial » bakoma tex key » bakoma tex 10.61 торрент » bakoma tex ключ к программе » telecharger bakoma tex » bakoma tex windows Latest News

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Differentiable over an interval [latex]I[/latex]; if [latex]f^{\prime \prime}>0[/latex] over [latex]I[/latex], then [latex]f[/latex] is concave up over [latex]I[/latex]; if [latex]f^{\prime \prime}constant multiple rulethe derivative of a constant [latex]c[/latex] multiplied by a function [latex]f[/latex] is the same as the constant multiplied by the derivative: [latex]\frac{d}{dx}(cf(x))=cf^{\prime}(x)[/latex]constant rulethe derivative of a constant function is zero: [latex]\frac{d}{dx}(c)=0[/latex], where [latex]c[/latex] is a constantcontinuity at a pointA function [latex]f(x)[/latex] is continuous at a point [latex]a[/latex] if and only if the following three conditions are satisfied: (1) [latex]f(a)[/latex] is defined, (2) [latex]\underset{x\to a}{\lim}f(x)[/latex] exists, and (3) [latex]\underset{x\to a}{\lim}f(x)=f(a)[/latex]continuity from the leftA function is continuous from the left at [latex]b[/latex] if [latex]\underset{x\to b^-}{\lim}f(x)=f(b)[/latex]continuity from the rightA function is continuous from the right at [latex]a[/latex] if [latex]\underset{x\to a^+}{\lim}f(x)=f(a)[/latex]continuity over an intervala function that can be traced with a pencil without lifting the pencil; a function is continuous over an open interval if it is continuous at every point in the interval; a function [latex]f(x)[/latex] is continuous over a closed interval of the form [latex][a,b][/latex] if it is continuous at every point in [latex](a,b)[/latex], and it is continuous from the right at [latex]a[/latex] and from the left at [latex]b[/latex]critical pointif [latex]f^{\prime}(c)=0[/latex] or [latex]f^{\prime}(c)[/latex] is undefined, we say that [latex]c[/latex] is a critical point of [latex]f[/latex]cross-sectionthe intersection of a plane and a solid objectcubic functiona polynomial of degree 3; that is, a function of the form [latex]f(x)=ax^3+bx^2+cx+d[/latex], where [latex]a \ne 0[/latex]decreasing on the interval [latex]I[/latex]a function decreasing on the interval [latex]I[/latex] if, for all [latex]x_1, \, x_2\in I, \, f(x_1)\ge f(x_2)[/latex] if [latex]x_1definite integrala primary operation of calculus; the area between the curve and the [latex]x[/latex]-axis over a given interval is a definite integraldensity functiona density function describes how mass is distributed throughout an object; it can be a linear density, expressed in terms of mass per unit length; an area density, expressed in terms of mass per unit area; or a volume density, expressed in terms of mass per unit volume; weight-density is also used to describe weight (rather than mass) per unit volumedependent variablethe output variable for a functionderivativethe slope of the tangent line to a function at a point, calculated by taking the limit of the difference quotient, is the derivativederivative functiongives the derivative of a function at each point in the domain of the original function for which the derivative is defineddifference quotientof a function [latex]f(x)[/latex] at [latex]a[/latex] is given by[latex]\dfrac{f(a+h)-f(a)}{h}[/latex] or [latex]\dfrac{f(x)-f(a)}{x-a}[/latex]difference rulethe derivative of the difference of a function [latex]f[/latex] and a function [latex]g[/latex] is the same as the difference of the derivative of [latex]f[/latex] and the derivative of [latex]g[/latex]: [latex]\frac{d}{dx}(f(x)-g(x))=f^{\prime}(x)-g^{\prime}(x)[/latex]differentiable at [latex]a[/latex]a function for which [latex]f^{\prime}(a)[/latex] exists is differentiable at [latex]a[/latex]differentiable on [latex]S[/latex]a function for which [latex]f^{\prime}(x)[/latex] exists for each [latex]x[/latex] in the open set. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX.

Modern alternatives to LaTeX : r/LaTeX - Reddit

TeXstudio VS TeXShop TeXstudio is a powerful, feature-rich LaTeX editor that offers extensive customization and support for advanced users, making it suitable for complex document preparation. In contrast, TeXShop provides a simpler, more user-friendly experience tailored for macOS users, ideal for smaller projects and those new to LaTeX. TeXstudio Pros: Feature-rich with extensive customization options Cross-platform compatibility Strong community support and plugins Integrated version control Advanced code completion and macros Cons: Can be overwhelming for beginners Requires some configuration to optimize Heavy for lower-end systems TeXShop Pros: Simple and user-friendly interface Optimized for macOS users Integrated PDF viewer and syncing Good for small to medium-sized projects Lightweight and easy to set up Cons: Limited to macOS Fewer advanced features compared to alternatives Not suitable for larger projects Compare TeXstudio Compare Gummi and TeXstudio and decide which is most suitable for you. Compare Kile and TeXstudio and decide which is most suitable for you. Compare TeX Live and TeXstudio and decide which is most suitable for you. Compare TeXmacs and TeXstudio and decide which is most suitable for you. Compare Texmaker and TeXstudio and decide which is most suitable for you. Compare TeXnicCenter and TeXstudio and decide which is most suitable for you. Compare TeXworks and TeXstudio and decide which is most suitable for you. Compare VerbTeX LaTeX Editor and TeXstudio and decide which is most suitable for you. Compare Overleaf and TeXstudio and decide which is most suitable for you.

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Feature-rich application to help programmers for building web apps with preset tags and commands. There is support for numerous languages including PHP, JavaScript, Python, HTML5, CSS3, and Ruby. The multiple panels interface is here for managing the workspace, snippets, and samples, exploring apps and viewing console, error, and terminal details. This program offers users convert line delimiters, run configurations, activate word completion mode, add tasks and bookmarks, and open resources. You can customize the…Aptana Studio Alternatives 6: Kate Kate is an intuitive text editor that features support for syntax highlighting and scripts, a wide range of programming languages, and an extensive configuration window. A well-organized interface is here and the program which is developed by Kate Team offers an interactive tooltip component. The users can manage their projects by creating folders and sort them by their name, opening order, or path. This utility offers you find C, C++, LISP, Latex, Haskell, Pascal, Lua, Ruby, and Python. You can…Kate Alternatives 7: Coda Coda is a straightforward web development utility that comes with various tools to design, test, and build your projects in an intuitive manner. It is specially designed to lighten your workload and simplify your workflow. You can quickly open a Terminal window, a new document, or establish connections with MySQL databases through a drop-down panel. A collection of books has access to various languages such as CSS, HTML, PHP, JQuery, JavaScript, and much more. Coda is developed by Panic Inc…Coda Alternatives 8: TextMate TextMate is a reliable Mac OS X text editor that is designed to writing code and markup and offers support for designers and programmers. You can use syntax highlight themes for different scripting languages with this unsophisticated text editor app. Here, adjusting the tab size, altering the scripting language, and accessing their customization options are possible.

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In the domain of [latex]f[/latex] and [latex]y=f(x)[/latex]half-lifeif a quantity decays exponentially, the half-life is the amount of time it takes the quantity to be reduced by half. It is given by [latex]\frac{(\text{ln}2)}{k}[/latex]higher-order derivativea derivative of a derivative, from the second derivative to the [latex]n[/latex]th derivative, is called a higher-order derivativeHooke’s lawthis law states that the force required to compress (or elongate) a spring is proportional to the distance the spring has been compressed (or stretched) from equilibrium; in other words, [latex]F=kx,[/latex] where [latex]k[/latex] is a constanthorizontal asymptoteif [latex]\underset{x\to \infty }{\lim}f(x)=L[/latex] or [latex]\underset{x\to −\infty }{\lim}f(x)=L[/latex], then [latex]y=L[/latex] is a horizontal asymptote of [latex]f[/latex]horizontal line testa function [latex]f[/latex] is one-to-one if and only if every horizontal line intersects the graph of [latex]f[/latex], at most, oncehydrostatic pressurethe pressure exerted by water on a submerged objecthyperbolic functionsthe functions denoted [latex]\sinh, \, \cosh, \, \tanh, \, \text{csch}, \, \text{sech}[/latex], and [latex]\coth[/latex], which involve certain combinations of [latex]e^x[/latex] and [latex]e^{−x}[/latex]implicit differentiationis a technique for computing [latex]\frac{dy}{dx}[/latex] for a function defined by an equation, accomplished by differentiating both sides of the equation (remembering to treat the variable [latex]y[/latex] as a function) and solving for [latex]\frac{dy}{dx}[/latex]increasing on the interval [latex]I[/latex]a function increasing on the interval [latex]I[/latex] if for all [latex]x_1, \, x_2\in I, \, f(x_1)\le f(x_2)[/latex] if [latex]x_1indefinite integralthe most general antiderivative of [latex]f(x)[/latex] is the indefinite integral of [latex]f[/latex]; we use the notation [latex]\displaystyle\int f(x) dx[/latex] to denote the indefinite integral of [latex]f[/latex]independent variablethe input variable for a functionindeterminate formswhen evaluating a limit, the forms [latex]0/0[/latex], [latex]\infty / \infty[/latex], [latex]0 \cdot \infty[/latex], [latex]\infty -\infty[/latex], [latex]0^0[/latex], [latex]\infty^0[/latex], and [latex]1^{\infty}[/latex] are considered indeterminate because further analysis is required to determine whether the limit exists and, if so, what its value isinfinite discontinuityAn infinite discontinuity occurs at a point [latex]a[/latex] if [latex]\underset{x\to a^-}{\lim}f(x)=\pm \infty[/latex] or [latex]\underset{x\to a^+}{\lim}f(x)=\pm \infty[/latex]infinite limitA function has an infinite limit at a point [latex]a[/latex] if it either increases or decreases without bound as it approaches [latex]a[/latex]infinite limit at infinitya function that becomes arbitrarily large as [latex]x[/latex] becomes largeinflection pointif [latex]f[/latex] is continuous at [latex]c[/latex] and [latex]f[/latex] changes concavity at [latex]c[/latex], the point [latex](c,f(c))[/latex] is an inflection point of [latex]f[/latex]initial value problema problem that requires finding a function [latex]y[/latex] that satisfies the differential equation [latex]\frac{dy}{dx}=f(x)[/latex] together with the initial condition [latex]y(x_0)=y_0[/latex]instantaneous rate of changethe rate of change of a function at any point along the function [latex]a[/latex], also called [latex]f^{\prime}(a)[/latex], or the derivative of the function at [latex]a[/latex]integrable functiona function is integrable if the limit defining the integral exists; in other words, if the limit of the Riemann sums as [latex]n[/latex] goes to infinity existsintegrandthe function to the right of the integration symbol; the integrand includes the function being integratedintegration by substitutiona technique for integration that allows

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Integration of functions that are the result of a chain-rule derivativeIntermediate Value TheoremLet [latex]f[/latex] be continuous over a closed bounded interval [latex][a,b][/latex]; if [latex]z[/latex] is any real number between [latex]f(a)[/latex] and [latex]f(b)[/latex], then there is a number [latex]c[/latex] in [latex][a,b][/latex] satisfying [latex]f(c)=z[/latex]intuitive definition of the limitIf all values of the function [latex]f(x)[/latex] approach the real number [latex]L[/latex] as the values of [latex]x(\ne a)[/latex] approach [latex]a[/latex], [latex]f(x)[/latex] approaches [latex]L[/latex]inverse functionfor a function [latex]f[/latex], the inverse function [latex]f^{-1}[/latex] satisfies [latex]f^{-1}(y)=x[/latex] if [latex]f(x)=y[/latex]inverse hyperbolic functionsthe inverses of the hyperbolic functions where [latex]\cosh[/latex] and [latex]\text{sech}[/latex] are restricted to the domain [latex][0,\infty)[/latex]; each of these functions can be expressed in terms of a composition of the natural logarithm function and an algebraic functioninverse trigonometric functionsthe inverses of the trigonometric functions are defined on restricted domains where they are one-to-one functionsiterative processprocess in which a list of numbers [latex]x_0,x_1,x_2,x_3, \cdots[/latex] is generated by starting with a number [latex]x_0[/latex] and defining [latex]x_n=F(x_{n-1})[/latex] for [latex]n \ge 1[/latex]jump discontinuityA jump discontinuity occurs at a point [latex]a[/latex] if [latex]\underset{x\to a^-}{\lim}f(x)[/latex] and [latex]\underset{x\to a^+}{\lim}f(x)[/latex] both exist, but [latex]\underset{x\to a^-}{\lim}f(x) \ne \underset{x\to a^+}{\lim}f(x)[/latex]laminaa thin sheet of material; laminas are thin enough that, for mathematical purposes, they can be treated as if they are two-dimensionalleft-endpoint approximationan approximation of the area under a curve computed by using the left endpoint of each subinterval to calculate the height of the vertical sides of each rectangleL’Hôpital’s ruleif [latex]f[/latex] and [latex]g[/latex] are differentiable functions over an interval [latex]a[/latex], except possibly at [latex]a[/latex], and [latex]\underset{x\to a}{\lim} f(x)=0=\underset{x\to a}{\lim} g(x)[/latex] or [latex]\underset{x\to a}{\lim} f(x)[/latex] and [latex]\underset{x\to a}{\lim} g(x)[/latex] are infinite, then [latex]\underset{x\to a}{\lim}\dfrac{f(x)}{g(x)}=\underset{x\to a}{\lim}\dfrac{f^{\prime}(x)}{g^{\prime}(x)}[/latex], assuming the limit on the right exists or is [latex]\infty[/latex] or [latex]−\infty[/latex]limit at infinitythe limiting value, if it exists, of a function as [latex]x\to \infty[/latex] or [latex]x\to −\infty[/latex]limits of integrationthese values appear near the top and bottom of the integral sign and define the interval over which the function should be integratedlinear approximationthe linear function [latex]L(x)=f(a)+f^{\prime}(a)(x-a)[/latex] is the linear approximation of [latex]f[/latex] at [latex]x=a[/latex]linear functiona function that can be written in the form [latex]f(x)=mx+b[/latex]local extremumif [latex]f[/latex] has a local maximum or local minimum at [latex]c[/latex], we say [latex]f[/latex] has a local extremum at [latex]c[/latex]local maximumif there exists an interval [latex]I[/latex] such that [latex]f(c)\ge f(x)[/latex] for all [latex]x\in I[/latex], we say [latex]f[/latex] has a local maximum at [latex]c[/latex]local minimumif there exists an interval [latex]I[/latex] such that [latex]f(c)\le f(x)[/latex] for all [latex]x\in I[/latex], we say [latex]f[/latex] has a local minimum at [latex]c[/latex]logarithmic differentiationis a technique that allows us to differentiate a function by first taking the natural logarithm of both sides of an equation, applying properties of logarithms to simplify the equation, and differentiating implicitlylogarithmic functiona function of the form [latex]f(x)=\log_b(x)[/latex] for some base [latex]b>0, \, b. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX.

typography - Alternatives to LaTeX - TeX - LaTeX Stack Exchange

[latex]S[/latex] is differentiable on [latex]S[/latex]differentiable functiona function for which [latex]f^{\prime}(x)[/latex] exists is a differentiable functiondifferentialthe differential [latex]dx[/latex] is an independent variable that can be assigned any nonzero real number; the differential [latex]dy[/latex] is defined to be [latex]dy=f^{\prime}(x) \, dx[/latex]differential formgiven a differentiable function [latex]y=f^{\prime}(x)[/latex], the equation [latex]dy=f^{\prime}(x) \, dx[/latex] is the differential form of the derivative of [latex]y[/latex] with respect to [latex]x[/latex]differentiationthe process of taking a derivativediscontinuity at a pointA function is discontinuous at a point or has a discontinuity at a point if it is not continuous at the pointdisk methoda special case of the slicing method used with solids of revolution when the slices are disksdomainthe set of inputs for a functiondoubling timeif a quantity grows exponentially, the doubling time is the amount of time it takes the quantity to double, and is given by [latex]\frac{(\text{ln}2)}{k}[/latex]end behaviorthe behavior of a function as [latex]x\to \infty[/latex] and [latex]x\to −\infty[/latex]epsilon-delta definition of the limit[latex]\underset{x\to a}{\lim}f(x)=L[/latex] if for every [latex]\varepsilon >0[/latex], there exists a [latex]\delta >0[/latex] such that if [latex]0even functiona function is even if [latex]f(−x)=f(x)[/latex] for all [latex]x[/latex] in the domain of [latex]f[/latex]exponentthe value [latex]x[/latex] in the expression [latex]b^x[/latex]exponential decaysystems that exhibit exponential decay follow a model of the form [latex]y={y}_{0}{e}^{\text{−}kt}[/latex]exponential growthsystems that exhibit exponential growth follow a model of the form [latex]y={y}_{0}{e}^{kt}[/latex]extreme value theoremif [latex]f[/latex] is a continuous function over a finite, closed interval, then [latex]f[/latex] has an absolute maximum and an absolute minimumFermat’s theoremif [latex]f[/latex] has a local extremum at [latex]c[/latex], then [latex]c[/latex] is a critical point of [latex]f[/latex]first derivative testlet [latex]f[/latex] be a continuous function over an interval [latex]I[/latex] containing a critical point [latex]c[/latex] such that [latex]f[/latex] is differentiable over [latex]I[/latex] except possibly at [latex]c[/latex]; if [latex]f^{\prime}[/latex] changes sign from positive to negative as [latex]x[/latex] increases through [latex]c[/latex], then [latex]f[/latex] has a local maximum at [latex]c[/latex]; if [latex]f^{\prime}[/latex] changes sign from negative to positive as [latex]x[/latex] increases through [latex]c[/latex], then [latex]f[/latex] has a local minimum at [latex]c[/latex]; if [latex]f^{\prime}[/latex] does not change sign as [latex]x[/latex] increases through [latex]c[/latex], then [latex]f[/latex] does not have a local extremum at [latex]c[/latex]frustuma portion of a cone; a frustum is constructed by cutting the cone with a plane parallel to the basefunctiona set of inputs, a set of outputs, and a rule for mapping each input to exactly one outputfundamental theorem of calculusthe theorem, central to the entire development of calculus, that establishes the relationship between differentiation and integrationfundamental theorem of calculus, part 1uses a definite integral to define an antiderivative of a functionfundamental theorem of calculus, part 2(also, evaluation theorem) we can evaluate a definite integral by evaluating the antiderivative of the integrand at the endpoints of the interval and subtractinggraph of a functionthe set of points [latex](x,y)[/latex] such that [latex]x[/latex] is

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Absolute extremumif [latex]f[/latex] has an absolute maximum or absolute minimum at [latex]c[/latex], we say [latex]f[/latex] has an absolute extremum at [latex]c[/latex]absolute maximumif [latex]f(c)\ge f(x)[/latex] for all [latex]x[/latex] in the domain of [latex]f[/latex], we say [latex]f[/latex] has an absolute maximum at [latex]c[/latex]absolute minimumif [latex]f(c)\le f(x)[/latex] for all [latex]x[/latex] in the domain of [latex]f[/latex], we say [latex]f[/latex] has an absolute minimum at [latex]c[/latex]absolute value function[latex]f(x) = |x| = \begin{cases} x, & x \ge 0 \\ -x, & x accelerationis the rate of change of the velocity, that is, the derivative of velocityalgebraic functiona function involving any combination of only the basic operations of addition, subtraction, multiplication, division, powers, and roots applied to an input variable [latex]x[/latex]amount of changethe amount of a function [latex]f(x)[/latex] over an interval [latex][x,x+h][/latex] is [latex]f(x+h)-f(x)[/latex]antiderivativea function [latex]F[/latex] such that [latex]F^{\prime}(x)=f(x)[/latex] for all [latex]x[/latex] in the domain of [latex]f[/latex] is an antiderivative of [latex]f[/latex]arc lengththe arc length of a curve can be thought of as the distance a person would travel along the path of the curveaverage rate of changeis a function [latex]f(x)[/latex] over an interval [latex][x,x+h][/latex] is [latex]\dfrac{f(x+h)-f(a)}{b-a}[/latex]average value of a function(or [latex]f_{\text{ave}}[/latex]) the average value of a function on an interval can be found by calculating the definite integral of the function and dividing that value by the length of the intervalbasethe number [latex]b[/latex] in the exponential function [latex]f(x)=b^x[/latex] and the logarithmic function [latex]f(x)=\log_b x[/latex]catenarya curve in the shape of the function [latex]y=a\text{cosh}(x\text{/}a)[/latex] is a catenary; a cable of uniform density suspended between two supports assumes the shape of a catenarycenter of massthe point at which the total mass of the system could be concentrated without changing the momentcentroidthe centroid of a region is the geometric center of the region; laminas are often represented by regions in the plane; if the lamina has a constant density, the center of mass of the lamina depends only on the shape of the corresponding planar region; in this case, the center of mass of the lamina corresponds to the centroid of the representative regionchain rulethe chain rule defines the derivative of a composite function as the derivative of the outer function evaluated at the inner function times the derivative of the inner functionchange of variablesthe substitution of a variable, such as [latex]u[/latex], for an expression in the integrandcomposite functiongiven two functions [latex]f[/latex] and [latex]g[/latex], a new function, denoted [latex]g\circ f[/latex], such that [latex](g\circ f)(x)=g(f(x))[/latex]concave downif [latex]f[/latex] is differentiable over an interval [latex]I[/latex] and [latex]f^{\prime}[/latex] is decreasing over [latex]I[/latex], then [latex]f[/latex] is concave down over [latex]I[/latex]concave upif [latex]f[/latex] is differentiable over an interval [latex]I[/latex] and [latex]f^{\prime}[/latex] is increasing over [latex]I[/latex], then [latex]f[/latex] is concave up over [latex]I[/latex]concavitythe upward or downward curve of the graph of a functionconcavity testsuppose [latex]f[/latex] is twice. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX. LaTeX Alternatives and Competitors. A comprehensive list of competitors and best alternatives to LaTeX.

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\ne 1[/latex] such that [latex]y=\log_b(x)[/latex] if and only if [latex]b^y=x[/latex]lower suma sum obtained by using the minimum value of [latex]f(x)[/latex] on each subintervalmarginal costis the derivative of the cost function, or the approximate cost of producing one more itemmarginal revenueis the derivative of the revenue function, or the approximate revenue obtained by selling one more itemmarginal profitis the derivative of the profit function, or the approximate profit obtained by producing and selling one more itemmathematical modelA method of simulating real-life situations with mathematical equationsmean value theoremif [latex]f[/latex] is continuous over [latex][a,b][/latex] and differentiable over [latex](a,b)[/latex], then there exists [latex]c \in (a,b)[/latex] such that[latex]f^{\prime}(c)=\dfrac{f(b)-f(a)}{b-a}[/latex]mean value theorem for integralsguarantees that a point [latex]c[/latex] exists such that [latex]f(c)[/latex] is equal to the average value of the functionmethod of cylindrical shellsa method of calculating the volume of a solid of revolution by dividing the solid into nested cylindrical shells; this method is different from the methods of disks or washers in that we integrate with respect to the opposite variablemomentif [latex]n[/latex] masses are arranged on a number line, the moment of the system with respect to the origin is given by [latex]M=\displaystyle\sum_{i=1}{n} {m}_{i}{x}_{i};[/latex] if, instead, we consider a region in the plane, bounded above by a function [latex]f(x)[/latex] over an interval [latex]\left[a,b\right],[/latex] then the moments of the region with respect to the [latex]x[/latex]– and [latex]y[/latex]-axes are given by [latex]{M}_{x}=\rho {\displaystyle\int }_{a}^{b}\frac{{\left[f(x)\right]}^{2}}{2}dx[/latex] and [latex]{M}_{y}=\rho {\displaystyle\int }_{a}^{b}xf(x)dx,[/latex] respectivelynatural exponential functionthe function [latex]f(x)=e^x[/latex]natural logarithmthe function [latex]\ln x=\log_e x[/latex]net change theoremif we know the rate of change of a quantity, the net change theorem says the future quantity is equal to the initial quantity plus the integral of the rate of change of the quantitynet signed areathe area between a function and the [latex]x[/latex]-axis such that the area below the [latex]x[/latex]-axis is subtracted from the area above the [latex]x[/latex]-axis; the result is the same as the definite integral of the functionNewton’s methodmethod for approximating roots of [latex]f(x)=0[/latex]; using an initial guess [latex]x_0[/latex], each subsequent approximation is defined by the equation [latex]x_n=x_{n-1}-\dfrac{f(x_{n-1})}{f^{\prime}(x_{n-1})}[/latex]number eas [latex]m[/latex] gets larger, the quantity [latex](1+(1/m))^m[/latex] gets closer to some real number; we define that real number to be [latex]e[/latex]; the value of [latex]e[/latex] is approximately 2.718282oblique asymptotethe line [latex]y=mx+b[/latex] if [latex]f(x)[/latex] approaches it as [latex]x\to \infty[/latex] or [latex]x\to −\infty[/latex]odd functiona function is odd if [latex]f(−x)=−f(x)[/latex] for all [latex]x[/latex] in the domain of [latex]f[/latex]one-sided limitA one-sided limit of a function is a limit taken from either the left or the rightone-to-one functiona function [latex]f[/latex] is one-to-one if [latex]f(x_1) \ne f(x_2)[/latex] if [latex]x_1 \ne x_2[/latex]optimization problemsproblems that are solved by finding the maximum or minimum value of a functionpartitiona set of points that divides an interval into subintervalspercentage errorthe relative error expressed as a percentageperiodic functiona function