The function (sin x)tan x (Continuation of Exercise 89.)a.

Chapter 4, Problem 90E

(choose chapter or problem)

The function\( (\sin x)^{\tan x}\) (Continuation of Exercise 89.)

a. Graph\( f(x)=(\sin x)^{\tan x}\) on the interval \(-7 \leq x \leq 7\). How do you account for the gaps in the graph? How wide are the gaps?

b. Now graph \(f\) on the interval \( 0<x<\pi\). The function is not defined \(at x=\pi / 2\), but the graph has no break at this point. What is going on? What value does the graph appear to give for \(f\) at  \(at x=\pi / 2\) ? (Hint: Use l'Hôpital's Rule to find \(\lim f\) as \(x \rightarrow(\pi / 2)^{-}\) and \(\left.x \rightarrow(\pi / 2)^{+} .\right)\)

c. Continuing with the graphs in part (b), find max \(f\) and min \(f\) as accurately as you can and estimate the values of \( x\) at which they are taken on.

Equation Transcription:

 

 

Text Transcription:

(sin x)^ tan x

f(x) = (sin x)^ tan x

-7 < or = x < or + 7

f

0< x< pi

x=pi/2

f

x=pi/2

lim f

x right arrow(pi/2)^-

x right arrow(pi/2)^+.)

f

x