1 Functions And Limits 2 Derivatives 3 Applications Of Differentiation 4 Integrals 5 Applications Of Integration 6 Inverse Functions 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Infinite Sequences And Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus 17 Second-order Differential Equations expand_more
2.1 Derivatives And Rates Of Change 2.2 The Derivative As A Function 2.3 Differentiation Formulas 2.4 Derivatives Of Trigonometric Functions 2.5 The Chain Rule 2.6 Implicit Differentiation 2.7 Rates Of Change In The Natural And Social Sciences 2.8 Related Rates 2.9 Linear Approximations And Differentials 2.R Review 2.P Problem Plus expand_more
Problem 1CC: Write an expression for the slope of the tangent line to the curve y=f(x) at the point (a,f(a)). Problem 2CC Problem 3CC Problem 4CC: Define the derivative fa. Discuss two ways of interpreting this number. Problem 5CC Problem 6CC Problem 7CC Problem 8CC Problem 9CC Problem 10CC Problem 11CC: Give several examples of how the derivative can be interpreted as a rate of change in physics,... Problem 12CC Problem 1TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 2TFQ Problem 3TFQ Problem 4TFQ Problem 5TFQ Problem 6TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 7TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 8TFQ Problem 9TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 10TFQ Problem 11TFQ Problem 12TFQ Problem 13TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 14TFQ Problem 15TFQ Problem 1E: The displacement in meters of an object moving in a straight line is given by s=1+2t+14t2, where t... Problem 2E: The graph of f is shown. State, with reasons, the numbers at which f is not differentiable. Problem 3E Problem 4E Problem 5E: The figure shows the graph of f,f, and f".Identify each curve, and explain your choice. Problem 6E Problem 7E: The total cost of repaying a student loan at an interest rate of r per year is C=f(r). a What is the... Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E: 1340 Calculate y. y=x2x+2x Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E Problem 29E: 1340 Calculate y. sin(xy)=x2y Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E: If f(t)=4t+1, find f"(2). Problem 42E Problem 43E: Find y" if x6+y6=1. Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E: How many tangent fines to the curve y=x/(x+1) pass through the point 1, 2? At which points do these... Problem 57E: If f(x)=(xa)(xb)(xc), show that f(x)f(x)=1xa+1xb+1xc Problem 58E Problem 59E Problem 60E: If f and g are the functions whose graphs are shown, let P(x)=f(x)g(x), P(x)=f(x)g(x), and... Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E: 6971 Find h in terms of f.and g. h(x)=f(x)g(x) Problem 71E Problem 72E Problem 73E: A particle moves on a vertical line so that its coordinate at time r is y=t312t+3,t0. a Find the... Problem 74E: The volume of a right circular cone is V=13r2h, where r is the radius of the base and h is the... Problem 75E: The mass of part of a wire is x(1+x) kilograms, where x is measured in meters from one end of the... Problem 76E: The cost, in dollars, of producing x units of a certain commodity is C(x)=920+2x0.02x2+0.00007x3 a... Problem 77E Problem 78E Problem 79E Problem 80E: A waterskier skis over the ramp shown in the figure at a speed of 30 ft/s. How fast is she rising as... Problem 81E Problem 82E Problem 83E: a Find the linearization of f(x)=1+3x3 at a=0. State the corresponding linear approximation and use... Problem 84E Problem 85E: A window has the shape of a square surmounted by a semicircle. The base of the window is measured as... Problem 86E: 8688 Express the limit as a derivative and evaluate. limx1x171x1 Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E: Show that the length of the portion of any tangent line to the asteroid x2/3+y2/3=a2/3 cut of by the... format_list_bulleted