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Chapter 1: Q. 79 (page 136)

Use the Squeeze Theorem to find the limits. Explain exactly how the Squeeze Theorem applies in each case.

limx鈫�0xsin1x

Short Answer

Expert verified

The limit of the given equation is 0.

Step by step solution

01

Step 1. Given information.

Consider the given question,

limx鈫�0xsin1x

02

Step 2. Apply squeeze theorem.

Range of sin1xor sinxis -1,1.

localid="1648747846089" -1鈮�sin1x鈮�1

Multiply x on all the sides,

localid="1648747856102" -1x鈮�xsin1x鈮�1x-x鈮�xsin1x鈮�x

Applying limits on all the sides as x鈫�0,

localid="1648747870827" limx鈫�0-x鈮�limx鈫�0xsin1x鈮�limx鈫�0x-0鈮�limx鈫�0xsin1x鈮�00鈮�limx鈫�0xsin1x鈮�0

Applying the Squeeze theorem,

=0

03

Step 3. Plot the graph.

Representing the graph, we get,

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