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Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please

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Inverse Functions Derivatives of Exponential Functions Logarithmic Functions Derivatives of Logarithmic Functions The Natural Logarithmic Function: Differentiation and Integration The Natural Exponential Function: Differentiation and Integration Exponential Growth and Decay Inverse Trigonometric Functions: Differentiation and Integration Hyperbolic Functions Indeterminate Forms and L'Hôpital's Rule Bases Other than e and their Applications Inverse Functions: Exponential, Logarithmic, and Trigonometric Functions Inverse Functions and Advanced Integration > Inverse Functions: Exponential, Logarithmic, an... Free to share, print, make copies and changes. Get yours at um=direct&utm_source=boundless

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Key terms binary the bijective base-2 numeral system, which uses only the digits 0 and 1 differentiable a function that has a defined derivative (slope) at each point differentiation the process of determining the derived function of a function e the base of the natural logarithm, … exponent the power to which a number, symbol or expression is to be raised:f or example, the 3 in x3. exponential any function that has an exponent as an independent variable function a relation in which each element of the domain is associated with exactly one element of the co-domain indeterminate not accurately determined or determinable inverse a function that undoes another function Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration

inverse a function that undoes another function irrational of a real number, that cannot be written as the ratio of two integers limit a value to which a sequence or function converges linear having the form of a line; straight logarithm the exponent by which another fixed value, the base, must be raised to produce that number meromorphic relating to or being a function of a complex variable that is analytic everywhere in a region except for singularities at each of which infinity is the limit and each of which is contained in a neighborhood where the function is analytic except for the singular point itself polynomial an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power tangent a straight line touching a curve at a single point without crossing it there transcendental of or relating to a number that is not the root of any polynomial that has positive degree and rational coefficients trigonometric relating to the functions used in trigonometry: sin, cos, tan, csc, cot, sec Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration

Inverse Functions If f maps X to Y, then f–1 maps Y back to X. Free to share, print, make copies and changes. Get yours at Wikimedia. CC BY-SA View on Boundless.comCC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/9/9d/Inverse_Functions_Domain_and_Range.pngView on Boundless.com Inverse Functions and Advanced Integration

A Function and its Inverse A function f and its inverse, f–1. Because f maps a to 3, the inverse f–1 maps 3 back to a. Free to share, print, make copies and changes. Get yours at Wikimedia. CC BY-SA View on Boundless.comCC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/c/c8/Inverse_Function.pngView on Boundless.com Inverse Functions and Advanced Integration

Graph of an Exponential Function Graph of the exponential function illustrating that its derivative is equal to the value of the function. Free to share, print, make copies and changes. Get yours at Wikimedia. CC BY-SA View on Boundless.comCC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Exp_tangent.svg/321px-Exp_tangent.svg.pngView on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Graph of Log Base 2 The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log2(8) = 3, because 2^3 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph:." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Plot of log2(x) The graph of the logarithm to base 2 crosses the x-axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log2(8) = 3, because 23 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it. Free to share, print, make copies and changes. Get yours at Wikipedia. "Binary_logarithm_plot_with_ticks.png." CC BY-SA View on Boundless.comCC BY-SA 4.0https://en.wikipedia.org/wiki/LogarithmView on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Graph of the Logarithmic Function The graph of the logarithm to base 2,. It crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log2(8) = 3 because 23 = 8. The graph approaches the y axis but does not meet or intersect it. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph:." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Taylor Polynomial The Taylor polynomials for only provide accurate approximations in the range −1 1, the Taylor polynomials of higher degree are worse approximations. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Taylor Polynomial." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Taylor Series Approximations For ln(1+x) The Taylor polynomials for ln(1 + x) only provide accurate approximations in the range −1 1, the Taylor polynomials of higher degree are worse approximations. Free to share, print, make copies and changes. Get yours at Wikipedia. "LogTay.png." CC BY-SA View on Boundless.comCC BY-SA 4.0https://en.wikipedia.org/wiki/Natural_logarithmView on Boundless.com Inverse Functions and Advanced Integration

Exponential Function The natural exponential function y = ex Free to share, print, make copies and changes. Get yours at Wikipedia. "Exp.png." CC BY-SA View on Boundless.comCC BY-SA 4.0https://en.wikipedia.org/wiki/Exponential_functionView on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Natural Exponential Function The natural exponential function. Notice what happens when you switch the position of the different variables. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph:." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Exponential Growth This graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth. Free to share, print, make copies and changes. Get yours at Wikipedia. "Exponential.png." CC BY-SA View on Boundless.comCC BY-SA 3.0https://en.wikipedia.org/wiki/Exponential_growthView on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Exponential Growth The graph illustrates how exponential growth (purple) surpasses both linear (red) and cubic (blue) growth. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph:." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Inverse Trig Functions of arctan and arccot The usual principal values of the arctan (red) and arccot (blue) functions graphed on the Cartesian plane. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Inverse Trig Functions." CC BY-SA c fe3b90816e13 View on Boundless.comCC BY-SA 3.0https:// 4c fe3b90816e13View on Boundless.com Inverse Functions and Advanced Integration

Interactive Graph: Inverse Trig Functions of arcsin and arccos The usual principal values of the arcsin (blue) and arccos (red) functions graphed on the Cartesian plane. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Inverse Trig Functions." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Inverse Functions and Advanced Integration

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration If function f has a domain of 0g is its inverse, what do we know what the domain of g? A) It is also 0 B) We don't have enough information. C) It is -100 D) It is 0

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration If function f has a domain of 0g is its inverse, what do we know what the domain of g? A) It is also 0 B) We don't have enough information. C) It is -100 D) It is 0

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration Calculate the derivative of 105x. A) 5*ln10 B) ln10*105x C) 5*ln10*105x D) 5*105x

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration Calculate the derivative of 105x. A) 5*ln10 B) ln10*105x C) 5*ln10*105x D) 5*105x

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration Which of the following statements about the graph of a logarithmic function is true? A) All of these answers. B) The graph is asymptotic to the y-axis. C) The graph crosses the x-axis at (1,0). D) The domain is all positive real numbers.

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration Which of the following statements about the graph of a logarithmic function is true? A) All of these answers. B) The graph is asymptotic to the y-axis. C) The graph crosses the x-axis at (1,0). D) The domain is all positive real numbers.

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration What is the derivative of log3x? A) 1/(3ln(x)) B) 3/ln(x) C) 1/(xln(3)) D) x/ln(3)

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration What is the derivative of log3x? A) 1/(3ln(x)) B) 3/ln(x) C) 1/(xln(3)) D) x/ln(3)

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration Find the derivative of lnx2. A) 2/x B) x/2 C) 2/x2 D) 1/(2x)

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration Find the derivative of lnx2. A) 2/x B) x/2 C) 2/x2 D) 1/(2x)

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration In medieval times, there were 10,000 people living in a city that was struck by a plague so that people began to die at an exponential rate daily. After 6 days, there were only 8,500 people living. How many were living after three weeks? A) 6661 B) 6141 C) 9220 D) 5660

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration In medieval times, there were 10,000 people living in a city that was struck by a plague so that people began to die at an exponential rate daily. After 6 days, there were only 8,500 people living. How many were living after three weeks? A) 6661 B) 6141 C) 9220 D) 5660

Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration Which of the following logarithmic bases is commonly used in computer science and information theory? A) 2 B) e C) 10 D) none of these answers

Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// Inverse Functions and Advanced Integration Which of the following logarithmic bases is commonly used in computer science and information theory? A) 2 B) e C) 10 D) none of these answers

Attribution Wiktionary. "inverse." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/inverse Wiktionary. "function." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/function Wikipedia. "Inverse function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Inverse_function Wikipedia. "Exponential function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Exponential_function Wiktionary. "tangent." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/tangent Wiktionary. "exponential." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/exponential Wiktionary. "e." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/e Wikipedia. "Logarithmic function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Logarithmic_function Wikipedia. "Logarithmic function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Logarithmic_function Wiktionary. "exponent." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/exponent Wiktionary. "binary." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/binary Wikipedia. "Logarithmic functions." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Logarithmic_functions Wikibooks. "Calculus/Derivatives of Exponential and Logarithm Functions." CC BY-SA BY-SA Wikipedia. "logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/logarithm Wiktionary. "e." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/e Wikipedia. "Natural logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Natural_logarithm Wikipedia. "Natural logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Natural_logarithm Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration

Wikipedia. "Natural logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Natural_logarithm Wiktionary. "transcendental." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/transcendental Wiktionary. "irrational." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/irrational Wikibooks. "Calculus/Derivatives of Exponential and Logarithm Functions." CC BY-SA BY-SA Boundless Learning. "Boundless." CC BY-SA BY-SA 3.0http:// Wiktionary. "e." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/e Wikipedia. "Exponential growth." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Exponential_growth Wikipedia. "Exponential growth." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Exponential_growth Wiktionary. "polynomial." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/polynomial Wiktionary. "linear." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/linear Wiktionary. "exponential." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/exponential Wikipedia. "List of integrals of inverse trigonometric functions." CC BY-SA BY-SA Wikipedia. "Differentiation of trigonometric functions." CC BY-SA BY-SA Wikipedia. "Inverse trigonometric functions." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Inverse_trigonometric_functions Wiktionary. "trigonometric." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/trigonometric Wikipedia. "Hyperbolic function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Hyperbolic_function Wiktionary. "inverse." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/inverse Wiktionary. "meromorphic." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/meromorphic Wikipedia. "L'Hôpital's rule." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/L'H%25C3%25B4pital's_rule Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration

Wikipedia. "Indeterminate form." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Indeterminate_form Wiktionary. "limit." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/limit Wiktionary. "indeterminate." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/indeterminate Wiktionary. "differentiable." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/differentiable Wikipedia. "Logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Logarithm Wikipedia. "Binary logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Binary_logarithm Wikipedia. "logarithm." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/logarithm Free to share, print, make copies and changes. Get yours at Inverse Functions and Advanced Integration