Answered: Let a > 0 be a real number and…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 52E

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Question

Let a > 0 be a real number and consider
the family of functions ƒ(x) = sin ax on the interval [0, ∏/a].
a. Graph ƒ, for a = 1, 2, and 3.
b. Let g(a) be the area of the region bounded by the graph
of ƒ and the x-axis on the interval [0, ∏/a]. Graph g for
0 < a < ∞ . Is g an increasing function, a decreasing
function, or neither?

Expert Solution

Step 1

Given that family of functions is ƒ(x) = sin ax, on the interval $[0, \frac{π}{a}]$ and $a > 0$ .

Answer(a):

For $a = 1$ , the function becomes ƒ(x) = sin x.

So, the graph of the function ƒ(x) = sin x in the interval $[0, \frac{π}{1}] o r [0, π]$ is:

Step 2

For $a = 2$ , the function becomes ƒ(x) = sin 2x.

So, the graph of the function ƒ(x) = sin 2x in the interval $[0, \frac{π}{2}]$ is:

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