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lim(x to 0) {(1+x)^((2)/(x))} (where {.}...

`lim_(x to 0) {(1+x)^((2)/(x))}` (where `{.}` denotes the fractional part of x) is equal to

A

1

B

`e`

C

`e^(-1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(1+x)^(2//x)=(1+x)^(2//x)-[(1+x)^(2//x)]`
Now, `underset(xto0)lim(1+x)^(2//x)=e^(2)`
or`underset(xto0)lim{(1+x)^(2//x)}=e^(2)-[e^(2)]=e^(2)-7`
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CENGAGE ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
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  9. lim(xto1) (nx^(n-1)-(n+1)x^(n)+1)/((e^(x)-e)sinpix), where n=100,is eq...

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  10. lim(xto0) (log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)=

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  16. lim(xto0) ((1+tanx)/(1+sinx))^(cosecx) is equal to

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  19. lim(ntooo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is equal to

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