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d. Let g(r) = r sec(r) Find g'(r). 57 JAZL

d. Let g(r) = r sec(r) Find g'(r). 57 JAZL

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2.4 Derivatives of other trigonometric functions Activity 2.4.4. Answer each of the following questions. Where a derivative is requested, be sure to label the derivative function with its name using proper notation. a. Let f(x) = 5 sec(x) – 2 csc(x). Find the slope of the tangent line to f at the point where x = b. Let p(z) = z² sec(z) – z cot(z). Find the instantaneous rate of change of p at the point where z = 1. tan(t) c. Let h(t) = 2e' cos(t). Find h'(t). t2 + 1 r sec(r) d. Let g(r) = 5r Find g'(r). e. When a mass hangs from a spring and is set in motion, the object's position oscillates in a way that the size of the oscillations decrease. This is usually called a damped oscillation. Suppose that for a particular object, its displacement from equilibrium (where the object sits at rest) is modeled by the function 15 sin(t) s(t) = Assume that s is measured in inches and t in seconds. Sketch a graph of this function for t 2 0 to see how it represents the situation described. Then compute ds/dt, state the units on this function, and explain what it tells you about the object's motion. Finally, compute and interpret s'(2).
Transcribed Image Text:2.4 Derivatives of other trigonometric functions Activity 2.4.4. Answer each of the following questions. Where a derivative is requested, be sure to label the derivative function with its name using proper notation. a. Let f(x) = 5 sec(x) – 2 csc(x). Find the slope of the tangent line to f at the point where x = b. Let p(z) = z² sec(z) – z cot(z). Find the instantaneous rate of change of p at the point where z = 1. tan(t) c. Let h(t) = 2e' cos(t). Find h'(t). t2 + 1 r sec(r) d. Let g(r) = 5r Find g'(r). e. When a mass hangs from a spring and is set in motion, the object's position oscillates in a way that the size of the oscillations decrease. This is usually called a damped oscillation. Suppose that for a particular object, its displacement from equilibrium (where the object sits at rest) is modeled by the function 15 sin(t) s(t) = Assume that s is measured in inches and t in seconds. Sketch a graph of this function for t 2 0 to see how it represents the situation described. Then compute ds/dt, state the units on this function, and explain what it tells you about the object's motion. Finally, compute and interpret s'(2).
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