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3. Consider the functions f: R → R defined by f(0) = 4 + sin 0 and g: R → R defined by g(0) = sin 20. A. Functions f and g both have an amplitude of 1. Explain. B. The maximum and minimum values of function f are 5 and 3 (respectively); the maximum and minimum values of function g are -1 and 1 (respectively). Explain. C. The period of function f is 27, whereas the period of function g is only 7. Explain.

3. Consider the functions f: R → R defined by f(0) = 4 + sin 0 and g: R → R defined by g(0) = sin 20. A. Functions f and g both have an amplitude of 1. Explain. B. The maximum and minimum values of function f are 5 and 3 (respectively); the maximum and minimum values of function g are -1 and 1 (respectively). Explain. C. The period of function f is 27, whereas the period of function g is only 7. Explain.

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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3. Consider the functions f: R → R defined by ƒ(0) = 4 + sin and g: R → R defined by g(0) sin 20. A. Functions f and g both have an amplitude of 1. Explain. B. The maximum and minimum values of function f are 5 and 3 (respectively); the maximum and minimum values of function g are -1 and 1 (respectively). Explain. C. The period of function f is 2π, whereas the period of function g is only π. Explain. = D. Since the period of function g is compressed in comparison to the period of function f, which would you expect to have a greater slope: the tangent line to function f at x = 0 or the tangent line to function g at x 0? Explain. (Note: since we have not yet developed explicit formulas for the derivatives of trigonometric functions, you should rely only upon your intuition regarding the shape of the graphs of functions f and g near x = 0.)
Transcribed Image Text:3. Consider the functions f: R → R defined by ƒ(0) = 4 + sin and g: R → R defined by g(0) sin 20. A. Functions f and g both have an amplitude of 1. Explain. B. The maximum and minimum values of function f are 5 and 3 (respectively); the maximum and minimum values of function g are -1 and 1 (respectively). Explain. C. The period of function f is 2π, whereas the period of function g is only π. Explain. = D. Since the period of function g is compressed in comparison to the period of function f, which would you expect to have a greater slope: the tangent line to function f at x = 0 or the tangent line to function g at x 0? Explain. (Note: since we have not yet developed explicit formulas for the derivatives of trigonometric functions, you should rely only upon your intuition regarding the shape of the graphs of functions f and g near x = 0.)
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