   Chapter 2.2, Problem 52E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Consider the function f(x) = tan 1 x . (a) Show that .f(x) = 0 for x = 1 π , 1 2 π , 1 3 π , ⋯ (b) Show that f(x) = 1 for x = 4 π , 4 5 π , 4 9 π , ⋯ (c) What can you conclude about lim x → 0 + tan 1 x ?

(a)

To determine

To show: The function, f(x)=0forx=1π,12π,13π....

Explanation

Given:

The function f(x)=tan1x.

Proof:

Substitute x=1π,12π,13π... for f(x)=tan1x.

Recall the fact that tan(nπ)=0 as the tangent function has period π.

Thus, for x=1π, the value of f(1π) is obtained as follows

(b)

To determine

To show: The function f(x)=1forx=4π,45π,49π....

(c)

To determine

To conclude: The value of limx0+tan1x.

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