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
2.1 A Preview Of Calculus 2.2 Finding Limits Graphically And Numerically 2.3 Evaluating Limits Analytically 2.4 Continuity And One-Sided Limits 2.5 Infinite Limits Chapter Questions expand_more
Problem 1E: Estimating Limits In Exercises 14, use a graphing utility to graph the function and visually... Problem 102E Problem 103E: Squeeze Theorem In your own words, explain the Squeeze Theorem. Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E: Finding a Limit In Exercises 5-18, find the limit. limx212x+33 Problem 15E Problem 16E: Finding a Limit In Exercises 5-18, find the limit. limx0(3x2)4 Problem 17E Problem 18E: Finding a Limit In Exercises 5-18, find the limit. limx55x+3 Problem 19E Problem 20E Problem 21E Problem 22E Problem 37E Problem 38E: Finding Limits In Exercises 19-22, find the limits. f(x)=x+7,g(x)=x2 (a) limx3f(x) (b) limx4g(x) (c)... Problem 39E Problem 40E Problem 23E Problem 24E Problem 25E: Finding a Limit of a Transcendental Function In Exercises 23-36, find the limit of the... Problem 26E Problem 27E: Finding a Limit of a Transcendental Function In Exercises 23-36, find the limit of the... Problem 28E: Finding a Limit of a Transcendental Function In Exercises 23-36, find the limit of the... Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E: Finding a Limit of a Transcendental Function In Exercises 23-36, find the limit of the... Problem 34E Problem 35E Problem 36E: Finding a Limit of a Transcendental Function In Exercises 23-36, find the limit of the... Problem 41E Problem 42E: Evaluating Limits In Exercises 37-40, use the information to evaluate the limits.... Problem 43E Problem 44E: Evaluating Limits In Exercises 37-40, use the information to evaluate the limits. limxcf(x)=27 (a)... Problem 45E: Finding a Limit In Exercises 41-46, write a sampler function that agrees with the given function at... Problem 46E: Finding a Limit In Exercises 41-46, write a sampler function that agrees with the given function at... Problem 47E Problem 48E Problem 49E Problem 50E: Finding a Limit In Exercises 41-46, write a sampler function that agrees with the given function at... Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E: Finding a Limit In Exercises 47-62, find the limit. limx3x2+x6x29 Problem 56E: Finding a Limit In Exercises 47-62, find the limit. limx2x2+2x8x2x2 Problem 57E: Finding a Limit In Exercises 47-62, find the limit. limx4x+53x4 Problem 58E: Finding a Limit In Exercises 47-62, find the limit. limx3x+12x3 Problem 59E Problem 60E Problem 61E: Finding a Limit In Exercises 47-62, find the limit. limx0[1/(3+x)](1/3)x Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E: Finding a Limit of a Transcendental Function In Exercises 63-76, find the limit of the... Problem 68E: Finding a Limit of a Transcendental Function In Exercises 63-76, find the limit of the... Problem 69E Problem 70E: Finding a Limit of a Transcendental Function In Exercises 63-76, find the limit of the... Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E: Finding a Limit of a Transcendental Function In Exercises 63-76, find the limit of the... Problem 78E Problem 79E: Finding a Limit of a Transcendental Function In Exercises 63-76, find the limit of the... Problem 80E Problem 81E: Graphical, Numerical, and Analytic Analysis In Exercises 77-86, use a graphing utility to graph the... Problem 82E: Graphical, Numerical, and Analytic Analysis In Exercises 77-86, use a graphing utility to graph the... Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E: Finding a Limit In Exercises 87-94, find limx0f(x+x)f(x)x f(x)=x24x Problem 93E Problem 94E: Finding a Limit In Exercises 9194, find limx0f(x+x)f(x)x. f(x)=x Problem 95E: Using the Squeeze Theorem In Exercises 95 and 96, use the Squeeze Theorem to find limxcf(x).... Problem 96E: Using the Squeeze Theorem In Exercises 95 and 96, use the Squeeze Theorem to find limxcf(x).... Problem 97E Problem 98E Problem 99E Problem 100E: Using the Squeeze Theorem In Exercises 97-100, use a graphing utility to graph the given function... Problem 101E: Functions That Agree at All but One Point (a) In the context of finding limits, discuss what is... Problem 105E Problem 104E: HOW DO YOU SEE IT? Would you use the dividing out technique or the rationalizing technique to find... Problem 107E: In Exercises 105 and 106, use the position function s(t)=16t2+500, which gives the height (in feet)... Problem 108E: In Exercises 105 and 106, use the position function s(t)=16t2+500, which gives the height (in feet)... Problem 106E Problem 109E: Free-Falling Object In Exercises 107 and 108, use the position function s(t)=4.9t2+200, which gives... Problem 110E Problem 111E Problem 112E Problem 113E: Prove that limxcb=b, where b and c are real numbers. Problem 114E Problem 115E Problem 116E Problem 117E Problem 118E: Proof (a) Prove that if limxc|f(x)|=0, then limxcf(x)=0. (Note: This is the converse of Exercise... Problem 119E Problem 120E Problem 121E Problem 122E Problem 123E Problem 124E Problem 125E Problem 126E Problem 127E Problem 128E: Piecewise Functions Let... Problem 129E Problem 130E: Approximation (a) Find limx01cosxx2. (b) Use your answer to part (a) to derive the approximation... format_list_bulleted