1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivative 5 Integration 6 Applications Of Integration 7 Integration Techniques 8 Sequences And Infinite Series 9 Power Series 10 Parametric And Polar Curves A Algebra Review B Proofs Of Selected Theorems expand_more
1.1 Review Of Functions 1.2 Representing Functions 1.3 Inverse, Exponential, And Logarithmic Functions 1.4 Trigonometric Functions And Their Inverses Chapter Questions expand_more
Problem 1QC Problem 2QC Problem 3QC Problem 4QC Problem 5QC Problem 6QC Problem 1E: For b 0, what are the domain and range of f(x) = bx? Problem 2E: Give an example of a function that is one-to-one on the entire real number line. Problem 3E: Explain why a function that is not one-to-one on an interval I cannot have an inverse function on I. Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E: How is the property bx+ y = bxby related to the property logb (xy) = logb x + logb y? Problem 9E: For b 0 with b 1, what are the domain and range of f(x) = logb x and why? Problem 10E: Express 25 using base e. Problem 11E: One-to-one functions 11. Find three intervals on which f is one-to-one, making each interval as... Problem 12E: Find four intervals on which f is one-to-one, making each interval as large as possible. Problem 13E: Sketch a graph of a function that is one-to-one on the interval (, 0 ] but is not one-to-one on (,... Problem 14E: Sketch a graph of a function that is one-to-one on the intervals (, 2], and [2, ) but is not... Problem 15E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 16E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 17E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 18E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 19E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 20E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 21E: Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)... Problem 22E Problem 23E Problem 24E Problem 25E: Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)... Problem 26E Problem 27E: Finding inverse functions a. Find the inverse of each function (on the given interval, if specified)... Problem 28E Problem 29E: Splitting up curves The unit circle x2 + y2 = 1 consists of four one-to-one functions, f1(x), f2(x),... Problem 30E: Splitting up curves The equation y4 = 4x2 is associated with four one-to-one functions f1(x), f2(x),... Problem 31E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 37E Problem 38E Problem 39E: Graphs of inverses Sketch the graph of the inverse function. 39. Problem 40E: Graphs of inverses Sketch the graph of the inverse function. 40. Problem 41E: Solving logarithmic equations Solve the following equations. 41. log10 x = 3 Problem 42E: Solving logarithmic equations Solve the following equations. 42. log5 x = 1 Problem 43E: Solving logarithmic equations Solve the following equations. 43. loggx=13 Problem 44E: Solving logarithmic equations Solve the following equations. 44. logb 125 = 3 Problem 45E: Solving logarithmic equations Solve the following equations. 45. ln x = 1 Problem 46E: Solving logarithmic equations Solve the following equations. 46. ln y = 3 Problem 47E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 48E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 49E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 50E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 51E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 52E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 53E: Solving equations Solve the following equations. 53. 7x = 21 Problem 54E: Solving equations Solve the following equations. 54. 2x = 55 Problem 55E: Solving equations Solve the following equations. 55. 33x4 = 15 Problem 56E: Solving equations Solve the following equations. 56. 53x = 29 Problem 57E: Using inverse relations One hundred grams of a particular radioactive substance decays according to... Problem 58E Problem 59E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 60E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 61E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 62E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 63E: Changing bases Convert the following expressions to the indicated base. 63. 2x using base e Problem 64E: Changing bases Convert the following expressions to the indicated base. 64. 3sin x using base e Problem 65E: Changing bases Convert the following expressions to the indicated base. 65. In |x| using base 5 Problem 66E: Changing bases Convert the following expressions to the indicated base. 66. log2 (x2 + 1) using base... Problem 67E: Changing bases Convert the following expressions to the indicated base. 67. a1/ln a using base e,... Problem 68E: Changing bases Convert the following expressions to the indicated base. 68. a1/log10a using base 10,... Problem 69E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 70E: Graphs of exponential functions The following figure shows the graphs of y = 2x, y = 3x, y = 2x, and... Problem 71E: Graphs of logarithmic functions The following figure shows the graphs of y = log2 x, y = log4 x, and... Problem 72E: Graphs of modified exponential functions Without using a graphing utility, sketch the graph of y =... Problem 73E: Graphs of modified logarithmic functions Without using a graphing utility, sketch the graph of y =... Problem 74E: Large intersection point Use any means to approximate the intersection point(s) of the graphs of... Problem 75E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 76E Problem 77E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 78E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 79E: Population model A culture of bacteria has a population of 150 cells when it is first observed. The... Problem 80E: Charging a capacitor A capacitor is a device that stores electrical charge. The charge on a... Problem 81E: Height and time The height in feet of a baseball hit straight up from the ground with an initial... Problem 82E: Velocity of a skydiver The velocity of a skydiver (in m/s) t seconds after jumping from a plane is... Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E: Inverse of composite functions a. Let g(x) = 2x + 3 and h(x) = x3. Consider the composite function... Problem 89E Problem 90E: Inverses of (some) cubics Finding the inverse of a cubic polynomial is equivalent to solving a cubic... Problem 91E format_list_bulleted