   Chapter 2.2, Problem 12E

Chapter
Section
Textbook Problem

Sketch the graph of the function and use it to determine the values of a for which lim x → a f(x) exists. f ( x ) = { 1 + sin x     if   x < 0 cos x     if   0 ≤ x ≤ π sin x     if   x>0

To determine

To sketch: The graph of f(x) and determine the value of a from the graph for which limxaf(x) exists.

Explanation

Given:

The function f(x)={1+sinxif x<0cosxif 0xπsinxif x>π.

Graph:

Draw the graph of f(x) as follows.

Draw the graph of 1 + sin x curve to the left of vertical axis since the interval is restricted that x < 0. Then draw the cosine curve between the interval 0xπ and then draw the sine curve for the interval x>π.

The graph of f(x) is shown below in Figure 1.

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