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 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 Indeterminate Forms And L'hôpital's Rule 5.7 The Natural Logarithmic Function: Integration 5.8 Inverse Trigonometric Functions: Integration 5.9 Hyperbolic Functions Chapter Questions expand_more
Problem 1E: CONCEPT CHECK Hyperbolic Functions Describe how the name hyperbolic function arose. Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 7E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 8E Problem 9E: Evaluating a Function In Exercises 5-10, evaluate the function. If the value is not a rational... Problem 10E Problem 11E Problem 12E: Verifying an Identity In Exercises 11-18, verify the identity. coshxsinhx=ex Problem 13E: Verifying an Identity In Exercises 11-18, verify the identity. tanh2x+sech2x=1 Problem 14E: Verifying an Identity In Exercises 11-18, verify the identity. coth2xcsch2x=1 Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E: Finding a Derivative In Exercises 25-34, find the derivative of the function. f(x)=cosh(8x+1) Problem 27E Problem 28E: Finding a Derivative In Exercises 25-34, find the derivative of the function. f(x)=tanh(4x2+3x) Problem 29E Problem 30E: Finding a Derivative In Exercises 25-34, find the derivative of the function. y=ln(tanhx2) Problem 31E: Finding a Derivative In Exercises 25-34, find the derivative of the function. h(t)=t6sinh(3t) Problem 32E Problem 33E Problem 34E: Finding a Derivative In Exercises 25-34, find the derivative of the function. g(x)=sech23x Problem 35E: Finding a Derivative In Exercises 25-34, find the derivative of the function. y=sinh(1x2),(1,0) Problem 36E: Finding an Equation of a Tangent Line In Exercises 35-38, find an equation of the tangent line to... Problem 37E: Finding an Equation of a Tangent Line In Exercises 35-38, find an equation of the tangent line to... Problem 38E: 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 41E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 42E: Finding Relative Extrema In Exercises 39-42, find the relative extrema of the function. Use a... Problem 43E: Catenary In Exercises 43 and 44, a model for a power cable suspended between two towers is given.... Problem 44E: Catenary In Exercises 43 and 44, a model for a power cable suspended between two towers is given.... Problem 45E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. cosh4xdx Problem 46E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sech23xdx Problem 47E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sinh(12x)dx Problem 48E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. coshxxdx Problem 49E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. cosh2(x1)sinh(x1)dx Problem 50E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. sinhx1+sinh2xdx Problem 51E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. coshxsinhxdx Problem 52E: Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral.... Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E: Evaluating a Definite Integral In Exercises 55-60, evaluate the definite integral. 1/21sech2(2x1)dx 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: Finding a Derivative In Exercises 65-74, find the derivative of the function. y=sech1(sinx),0x/2 Problem 72E: Finding a Derivative In Exercises 65-74, find the derivative of the function. y=coth1(e2x) 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: Proof Prove that tanh1x=12ln(1+x1x),1x1 Problem 96E Problem 97E Problem 98E Problem 99E Problem 100E Problem 101E Problem 102E Problem 103E Problem 104E Problem 105E Problem 106E: PUTNAM EXAM CHALLENGE Prove or disprove: there is at least one straight line normal to the graph of... format_list_bulleted