T Diagonostic Tests 1 Functions And Limits 2 Derivatives 3 Applications Of Differentiation 4 Integrals 5 Applications Of Integration 6 Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Infinite Sequences And Series A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-Degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G Complex Numbers expand_more
1.1 Four Ways To Represent A Function 1.2 Mathematical Models: A Catalog Of Essential Functions 1.3 New Functions From Old Functions 1.4 The Tangent And Velocity Problems 1.5 The Limit Of A Function 1.6 Calculating Limits Using The Limit Laws 1.7 The Precise Definition Of A Limit 1.8 Continuity Chapter Questions expand_more
Problem 1E Problem 2E: Explain what it means to say that limx1f(x)=3andlimx1+f(x)=7 In this situation is it possible that... Problem 3E: Explain the meaning of each of the following. (a) limx3f(x)= (b) limx4+f(x)= Problem 4E: Use the given graph of f to state the value of each quantity, if it exists. If it does not exist,... Problem 5E: For the function f whose graph is given, state the value of each quantity, if it exists. If it does... Problem 6E: For the function h whose graph is given, state the value of each quantity, if it exists. If it does... Problem 7E: For the function g whose graph is given, state the value of each quantity, if it exists. If it does... Problem 8E: For the function A whose graph is shown, state the following. (a) limx3A(x) (b) limx2A(x) (c)... Problem 9E: For the function f whose graph is shown, state the following. (a) limx7f(x) (b) limx3f(x) (c)... Problem 10E: A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount f(t) of... Problem 11E: Sketch the graph of the function and use it to determine the values of a for which limxa f(x)... Problem 12E: Sketch the graph of the function and use it to determine the values of a for which limxa f(x)... Problem 13E: Use the graph of the function f to state the value of each limit, if it exists. If it does not... Problem 14E: Use the graph of the function f to state the value of each limit, if it exists. If it does not... Problem 15E: Sketch the graph of an example of a function f that satisfies all of the given conditions. 15.... Problem 16E: Sketch the graph of an example of a function f that satisfies all of the given conditions. 16.... Problem 17E: Sketch the graph of an example of a function f that satisfies all of the given conditions. 17.... Problem 18E: Sketch the graph of an example of a function f that satisfies all of the given conditions. 18.... Problem 19E: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct... Problem 20E: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct... Problem 21E: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct... Problem 22E: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct... Problem 23E Problem 24E Problem 25E: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to... Problem 26E: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to... Problem 27E Problem 28E Problem 29E: Determine the infinite limit. 29. limx5+x+1x5 Problem 30E: Determine the infinite limit. 30. limx5x+1x5 Problem 31E Problem 32E: Determine the infinite limit. 32. limx3x(x3)5 Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E: Determine the infinite limit. 37. limx2xcscx Problem 38E Problem 39E: Determine the infinite limit. 39. limx2+x22x8x25x+6 Problem 40E Problem 41E: Determine limx11x31and limx1+1x31 (a) by evaluating f(x) = 1/(x3 1) for values of x that approach 1... Problem 42E Problem 43E: (a) Evaluate the function f(x) = x2 (2x/1000) for x = 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05, and... Problem 44E: (a) Evaluate h(x) = (tan x x)/x3 for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005. (b) Guess the value of... Problem 45E: Graph the function f(x) = sin(/x) of Example 4 in the viewing rectangle [1, 1] by [1, 1]. Then zoom... Problem 46E: Consider the function f(x)=tan1x. (a) Show that f(x) = 0 for x=1,12,13, (b) Show that f(x) = 1 for... Problem 47E Problem 48E Problem 49E: (a) Use numerical and graphical evidence to guess the value of the limit limx1x31x1 (a) How close to... format_list_bulleted