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Chapter 3: Q. 47 (page 311)

Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L鈥橦opital鈥檚 rule, and some are not.

limx鈫�0tan-1xsinx.

Short Answer

Expert verified

The exact value of the limitlimx鈫�0tan-1xsinxis,1.

Step by step solution

01

Step 1. Given information

limx鈫�0tan-1xsinx.

02

Step 2. The limit using L'Hopital's rule is given below:

limx鈫�0tan-1xsinx=limx鈫�011+x2cosx [L'Hopital's rule]

=limx鈫�011+x2cosx=11+02cos0=11=1

Therefore, the exact value is,1.

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