1 Foundation For Calculus: Functions And Limits 2 Key Concept: The Derivative 3 Short-cuts To Differentiation 4 Using The Derivative 5 Key Concept: The Definite Integral 6 Constructing Antiderivatives 7 Integration 8 Using The Definite Integral 9 Sequences And Series 10 Approximating Functions Using Series 11 Differential Equations 12 Functions Of Several Variables 13 A Fundamental Tool: Vectors 14 Differentiating Functions Of Several Variables 15 Optimization: Local And Global Extrema 16 Integrating Functions Of Several Variables 17 Parameterization And Vector Fields 18 Line Integrals 19 Flux Integrals And Divergence 20 The Curl And Stokes’ Theorem 21 Parameters, Coordinates, And Integrals expand_more
2.1 How Do We Measure Speed? 2.2 The Derivative At A Point 2.3 The Derivative Function 2.4 Interpretations Of The Derivative 2.5 The Second Derivative 2.6 Differentiability Chapter Questions expand_more
Problem 1E: For the graphs in Exercises 12, list the x-values for which the function appears to be (a) Not... Problem 2E: For the graphs in Exercises 12, list the x-values for which the function appears to be (a) Not... Problem 3E: In Exercises 34, does the function appear to be differentiable on the interval of x-values shown? Problem 4E: In Exercises 34, does the function appear to be differentiable on the interval of x-values shown? Problem 5E: In Exercises 57, decide if the function is differentiable at x = 0. Try zooming in on a graphing... Problem 6E: In Exercises 57, decide if the function is differentiable at x = 0. Try zooming in on a graphing... Problem 7E: In Exercises 57, decide if the function is differentiable at x = 0. Try zooming in on a graphing... Problem 8E: Decide if the functions in Problems 810 are differentiable at x = 0. Try zooming in on a graphing... Problem 9E: Decide if the functions in Problems 810 are differentiable at x = 0. Try zooming in on a graphing... Problem 10E: Decide if the functions in Problems 810 are differentiable at x = 0. Try zooming in on a graphing... Problem 11E: In each of the following cases, sketch the graph of a continuous function f(x) with the given... Problem 12E: Look at the graph of f(x) = (x2 + 0.0001)12 shown in Figure 2.64. The graph of f appears to have a... Problem 13E: The acceleration due to gravity, g, varies with height above the surface of the earth, in a certain... Problem 14E: An electric charge, Q, in a circuit is given as a function of time, t, by Q={Cfort0Cet/RCfort0,... Problem 15E: A magnetic field, B, is given as a function of the distance, r, from the center of a wire as... Problem 16E Problem 17E: Graph the function defined by g(r)={1+cos(r/2)for2r20forr2orr2. (a) Is g continuous at r = 2?... Problem 18E: The potential, , of a charge distribution at a point on the y-axis is given by... Problem 19E: Sometimes, odd behavior can be hidden beneath the surface of a rather normal-looking function.... Problem 20E: Figure 2.65 shows graphs of four useful but non differentiable functions: the step, the sign, the... Problem 21E: In Problems 2122, explain what is wrong with the statement. A function f that is not differentiable... Problem 22E: In Problems 2122, explain what is wrong with the statement. If f is not differentiable at a point... Problem 23E: In Problems 2325, give an example of: A continuous function that is not differentiable at x = 2. Problem 24E: In Problems 2325, give an example of: An invertible function that is not differentiable at x = 0. Problem 25E: In Problems 2325, give an example of: A rational function that has zeros at x=1 and is not... Problem 26E: Are the statements in Problems 2630 true or false? If a statement is true, give an example... Problem 27E: Are the statements in Problems 2630 true or false? If a statement is true, give an example... Problem 28E: Are the statements in Problems 2630 true or false? If a statement is true, give an example... Problem 29E: Are the statements in Problems 2630 true or false? If a statement is true, give an example... Problem 30E: Are the statements in Problems 2630 true or false? If a statement is true, give an example... Problem 31E: Which of the following would be a counterexample to the statement: If f is differentiable at x = a... format_list_bulleted