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
3.1 The Derivative And The Tangent Line Problem 3.2 Basic Differentiation Rules And Rates Of Change 3.3 Product And Quotient Rules And Higher-order Derivatives 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives Of Inverse Functions 3.7 Related Rates 3.8 Newton's Method Chapter Questions expand_more
Problem 1E: Tangent Line Describe how to find the slope of the tangent line to the graph of a function at a... Problem 2E: Notation List four notation alternatives to f(x). Problem 3E: Derivative Describe how to find the derivative of a function using the limit process. Problem 4E Problem 5E: Estimating Slope In Exercises 5 and 6, estimate the slope of the graph at the points (x1,y1) and... Problem 6E: Estimating Slope In Exercises 5 and 6, estimate the slope of the graph at the points (x1,y1) and... Problem 7E Problem 8E: Slopes of Secant Lines In Exercises 7 and 8, use the graph shown in the figure. To print an enlarged... Problem 9E Problem 10E: Finding the Slope of a Tangent Line In Exercises 9-14, find the slope of the tangent line to the... Problem 11E: Finding the Slope of a Tangent Line In Exercises 9-14, find the slope of the tangent line to the... Problem 12E: Finding the Slope of a Tangent Line In Exercises 9-14, find the slope of the tangent line to the... Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E: Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function... Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E: Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function... Problem 27E: Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function... Problem 28E: Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function... Problem 29E: Finding an Equation of a Tangent Line In Exercises 29-36, (a) find an equation of the tangent line... Problem 30E: Finding an Equation of a Tangent Line In Exercises 29-36, (a) find an equation of the tangent line... Problem 31E: Finding an Equation of a Tangent Line In Exercises 29-36, (a) find an equation of the tangent line... Problem 32E: Finding an Equation of a Tangent Line In Exercises 29-36, (a) find an equation of the tangent line... Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E: Finding an Equation of a Tangent Line In Exercises 37-42, find an equation of the line that is... Problem 38E: Finding an Equation of a Tangent Line In Exercises 37-42, find an equation of the line that is... Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 44E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 45E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 46E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 47E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 48E: Sketching a Derivative In Exercises 43-48, sketch the graph of f. Explain how you found your answer. Problem 49E: Sketching a Graph Sketch a graph of a function whose derivative is always negative. Explain how you... Problem 50E Problem 51E: Domain of the Derivative Do f and f always have the same domain? Explain. Problem 52E: Symmetry of a Graph A function f is symmetric with respect to the origin. Is f necessarily symmetric... Problem 53E: Using a Tangent Line The tangent line to the graph of the graph of y=g(x) at the point (4, 5) passes... Problem 54E Problem 55E Problem 56E: Working Backwards In Exercises 55-58, the limit represents f'(c) for a function f and a number c... Problem 57E: Working Backwards In Exercises 55-58, the limit represents f'(c) for a function f and a number c... Problem 58E: Working Backwards In Exercises 55-58, the limit represents f'(c) for a function f and a number c... Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E: HOW DO YOU SEE IT? The figure shows the graph of g (a) g(0)= (b) g(3)= (c) What can you conclude... Problem 65E Problem 66E: Graphical Reasoning Consider the function f(x)=13x3 (a) Use a graphing utility to graph the function... Problem 67E Problem 68E Problem 69E Problem 70E: Using the Alternative Form of the Derivative In Exercises 69-76, use the alternative form of the... Problem 71E Problem 72E Problem 73E: Using the Alternative Form of the Derivative In Exercises 69-76, use the alternative form of the... Problem 74E Problem 75E Problem 76E: Using the Alternative Form of the Derivative In Exercises 69-76, use the alternative form of the... Problem 77E Problem 78E: Determining Differentiability In Exercises 77-80, describe the x -values at which f is... Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E: Determining Differentiability In Exercises 85-88, find the derivatives from the left and from the... Problem 87E Problem 88E Problem 89E: Determining Differentiability In Exercises 89 and 90, determine whether the function is... Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E: True or False? In Exercises 93-96, determine whether the statement is true or false. If it is false,... Problem 95E Problem 96E Problem 97E Problem 98E: Writing Use a graphing utility to graph the two functions f(x)=x2+1 and g(x)=x+1 in the same viewing... format_list_bulleted