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
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 Chapter Questions expand_more
Problem 1E: A particle moves according to a law of motion s = f(t), t 0, where t is measured in seconds and s... Problem 2E: A particle moves according to a law of motion s = f(t), t 0, where t is measured in seconds and s... Problem 3E: A particle moves according to a law of motion s = f(t), t 0, where t is measured in seconds and s... Problem 4E: A particle moves according to a law of motion s = f(t), t 0, where t is measured in seconds and s... Problem 5E Problem 6E: Graphs of the position functions of two particles are shown, where t is measured in seconds. When is... Problem 7E: The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level... Problem 8E: If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is... Problem 9E: If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height... Problem 10E Problem 11E: (a) A company makes computer chips from square wafers of silicon. It wants to keep the side length... Problem 12E Problem 13E: (a) Find the average rate of change of the area of a circle with respect to its radius r as r... Problem 14E: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60... Problem 15E: A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4r2) with... Problem 16E Problem 17E: The mass of the part of a metal rod that lies between its left end and a point x meters to the right... Problem 18E: If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then... Problem 19E: The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t... Problem 20E: Newtons Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a... Problem 21E: The force F acting on a body with mass m and velocity v is the rate of change of momentum: F =... Problem 22E: Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At... Problem 23E: Boyles Law states that when a sample of gas is compressed at a constant temperature, the product of... Problem 24E Problem 25E: The table gives the population of the world P(t), in millions, where t is measured in years and t =... Problem 26E: The table shows how the average age of first marriage of Japanese women has varied since 1950. t... Problem 27E Problem 28E Problem 29E Problem 30E: The cost function for a certain commodity is C(q)=84+0.16q0.0006q2+0.000003q3 (a) Find and interpret... Problem 31E: If p(x) is the total value of the production when there are x workers in a plant, then file average... Problem 32E: If R denotes the reaction of the body to some stimulus of strength x, the sensitivity S is defined... Problem 33E Problem 34E Problem 35E: In the study of ecosystems, predator-prey models are often used to study the interaction between... Problem 36E format_list_bulleted