1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivatives 5 Integration 6 Applications Of Integration 7 Integration Techniques 8 Sequences And Infinite Series 9 Power Series 10 Parametric And Polar Curves 11 Vectors And Vector-valued Functions 12 Functions Of Several Variables 13 Multiple Integration 14 Vector Calculus D1 Differential Equations D2 Second-order Differential Equations A Algebra Review expand_more
3.1 Introducing The Derivative 3.2 Working With Derivatives 3.3 Rules Of Differentiation 3.4 The Product And Quotient Rules 3.5 Derivatives Of Trigonometric Functions 3.6 Derivatives As Rates Of Change 3.7 The Chain Rule 3.8 Implicit Differentiation 3.9 Derivatives Of Logarithmic And Exponential Functions 3.10 Derivatives Of Inverse Trigonometric Functions 3.11 Related Rates Chapter Questions expand_more
Problem 1E: Use definition (1) (p. 127) for the slope of a tangent line to explain how slopes of secant lines... Problem 2E: Explain why the slope of a secant line can be interpreted as an average rate of change. Problem 3E: Explain why the slope of the tangent line can be interpreted as an instantaneous rate of change. Problem 4E Problem 5E: Given a function f and a point a in its domain, what does f(a) represent? Problem 6E: Explain the relationships among the slope of a tangent line, the instantaneous rate of change, and... Problem 7E Problem 8E Problem 9E: Equations of tangent lines by definition (1) a. Use definition (1) (p. 127) to find the slope of the... Problem 10E: Equations of tangent lines by definition (1) a. Use definition (1) (p. 127) to find the slope of the... Problem 11E: Equations of tangent lines by definition (1) a. Use definition (1) (p. 127) to find the slope of the... Problem 12E Problem 13E: Equations of tangent lines by definition (1) a. Use definition (1) (p. 127) to find the slope of the... Problem 14E: Equations of tangent lines by definition (1) a. Use definition (1) (p. 127) to find the slope of the... Problem 15E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 16E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 17E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 18E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 19E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 20E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 21E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 22E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 23E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 24E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 25E: Equations of tangent lines by definition (2) a. Use definition (2) (p. 129) to find the slope of the... Problem 26E Problem 27E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 28E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 29E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 30E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 31E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 32E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 33E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 34E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 35E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 36E: Derivatives and tangent lines a. For the following functions and values of a, find f(a). b.... Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E: A derivative formula a. Use the definition of the derivative to determine ddx(ax2+bx+c), where a, b,... Problem 42E: A derivative formula a. Use the definition of the derivative to determine ddx(ax+b), where a and b... Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 48E: Slope of a line Consider the line f(x) = mx + b, where m and b are constants. Show that f(x) = m for... Problem 49E: Calculating derivatives a. For the following functions, find f using the definition. b. Determine an... Problem 50E: Calculating derivatives a. For the following functions, find f using the definition. b. Determine an... Problem 51E: Calculating derivatives a. For the following functions, find f using the definition. b. Determine an... Problem 52E: Calculating derivatives a. For the following functions, find f using the definition. b. Determine an... Problem 53E: Analyzing slopes Use the points A, B, C, D, and E in the following graphs to answer these questions.... Problem 54E: Analyzing slopes Use the points A, B, C, D, and E in the following graphs to answer these questions.... Problem 55E: Power and energy Energy is the capacity to do work, and power is the rate at which energy is used or... Problem 56E: Population of Las Vegas Let p(t) represent the population of the Las Vegas metropolitan area t years... Problem 57E: Find the function The following limits represent the slope of a curve y = f(x) at the point (a,... Problem 58E: Find the function The following limits represent the slope of a curve y = f(x) at the point (a,... Problem 59E: Find the function The following limits represent the slope of a curve y = f(x) at the point (a,... Problem 60E: Find the function The following limits represent the slope of a curve y = f(x) at the point (a,... Problem 61E Problem 62E: Looking ahead: Derivative of xn Use the definition f(x)=limh0f(x+h)f(x)h to find f(x) for the... Problem 63E Problem 64E: Approximating derivatives Assuming the limit exists, the definition of the derivative... Problem 65E: Approximating derivatives Assuming the limit exists, the definition of the derivative... Problem 66E Problem 67E: Approximating derivatives Assuming the limit exists, the definition of the derivative... format_list_bulleted