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 tangen 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.)
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 tangen 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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please help with part D.
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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