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Evaluatelim(xto pi//4) (2-tanx)^(1//1n(t...

Evaluate`lim_(xto pi//4) (2-tanx)^(1//1n(tanx))`

A

16

B

8

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
`e^(-1)`
`underset(xto pi//4)lim(2-tanx)^(1//1n(tanx))`
`=e^(underset(xto pi//4)lim(2-tanx-1)xx(1)/(1ntanx))" "(1^(oo)" form")`
`=e^(underset(xto pi//4)lim((1-tanx))/((1ntanx)))`
`=e^(underset(xto pi//4)lim(-sec^(2)x)/((1)/(tanx)sec^(2)x))`
`=e^(-underset(xto pi//4)limtanx)`
`=e^(-1)`
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