1 Preparation For Calculus 2 Limits And Their Properties 3 Differentiation 4 Applications Of Differentiation 5 Integration 6 Differential Equations 7 Applications Of Integration 8 Integration Techniques, L’ho?pital’s Rule, And Improper Integrals 9 Infinite Series 10 Conics, Parametric Equations, And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-Valued Functions 13 Functions Of Several Variables 14 Multiple Integration 15 Vector Analysis expand_more
5.1 Antiderivatives And Indefinite Integration 5.2 Area 5.3 Riemann Sums And Definite Integrals 5.4 The Fundamental Theorem Of Calculus 5.5 Integration By Substitution 5.6 Numerical Integration 5.7 The Natural Logarithmic Function: Integration 5.8 Inverse Trigonometric Functions: Integration 5.9 Hyperbolic Functions Chapter Questions expand_more
Problem 1E Problem 2E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 3E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 4E Problem 5E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 6E Problem 7E: Verifying an Identity In Exercises 11-18, verify the identity. tanh2x+sech2x=1 Problem 8E: Verifying an Identity In Exercises 11-18, verify the identity. coth2xcsch2x=1 Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E: Finding a Derivative In Exercises 25-34, find the derivative of the function. f(x)=cosh(8x+1) Problem 25E Problem 26E: Finding a Derivative In Exercises 25-34, find the derivative of the function. f(x)=tanh(4x2+3x) Problem 27E Problem 28E: Finding a Derivative In Exercises 25-34, find the derivative of the function. y=ln(tanhx2) Problem 29E Problem 30E Problem 31E Problem 32E: Finding a Derivative In Exercises 25-34, find the derivative of the function. g(x)=sech23x Problem 33E: Finding a Derivative In Exercises 25-34, find the derivative of the function. y=sinh(1x2),(1,0) Problem 34E: Finding an Equation of a Tangent Line In Exercises 35-38, find an equation of the tangent line to... Problem 35E: Finding an Equation of a Tangent Line In Exercises 35-38, find an equation of the tangent line to... Problem 36E: Finding an Equation of a Tangent Line In Exercises 35-38, find an equation of the tangent line to... Problem 39E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 40E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 37E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 38E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 41E: Catenary In Exercises 43 and 44, a model for a power cable suspended between two towers is given.... Problem 42E: Catenary In Exercises 43 and 44, a model for a power cable suspended between two towers is given.... Problem 43E Problem 44E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sech23xdx Problem 45E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sinh(12x)dx Problem 46E Problem 47E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. cosh2(x1)sinh(x1)dx Problem 48E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sinhx1+sinh2xdx Problem 49E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. coshxsinhxdx Problem 50E Problem 53E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral.... Problem 51E Problem 52E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E: HOW DO YOU SEE IT? Use the graphs of f and g shown in the figures to answer the following. (a)... Problem 65E Problem 66E Problem 67E Problem 68E: Finding a Derivative In Exercises 65-74, find the derivative of the function. f(x)=coth1(x2) Problem 69E: Finding a Derivative In Exercises 65-74, find the derivative of the function. y=sinh1(tanx) Problem 70E: Finding a Derivative In Exercises 65-74, find the derivative of the function. y=tanh1(sin2x) Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E Problem 99E: Proof Prove that tanh1x=12ln(1+x1x),1x1 Problem 100E Problem 101E Problem 102E Problem 103E Problem 104E Problem 105E Problem 106E Problem 107E Problem 108E Problem 109E Problem 110E: PUTNAM EXAM CHALLENGE Prove or disprove: there is at least one straight line normal to the graph of... format_list_bulleted