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The value of lim(xrarr oo) 1+(1)/(x^n)^x...

The value of `lim_(xrarr oo) 1+(1)/(x^n)^x,ngt 0`, is

A

`1, if n lt 1`

B

`1,if n gt 1`

C

`e,if n gt 1`

D

`e,if n lt 1`

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,
`lim_(xto oo) (1+(1)/x^n)^x=e^(lim_(xtooo)(x)/(x^n))=e^(lim_(xto oo)x^(1-n)= {(e^(0)=1,,"if " ngt1,,),(e,,"if " n=1,,),(oo,,"if " nlt1,,):}`
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