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lim(xrarroo) [x-log(e)((e^(x)+e^(-x))/(2...

`lim_(xrarroo) [x-log_(e)((e^(x)+e^(-x))/(2))]=`

A

`log_(e)4`

B

0

C

`log_(e)2`

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xrarroo)(lim)[x-log_(e)((e^(x)+e^(-x))/(2))]`
`=underset(xrarroo)(lim)[x-log_(e)e^(x)((1+e^(-2x))/(2))]`
`=underset(xrarroo)(lim)[x-x-log_(e)((1+e^(-2x))/(2))]`
`=-log_(e)((1)/(2))=log_(2)2`
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