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For x in R ,("lim")(xvecoo)((x-3)/(x+2)...

For `x in R ,("lim")_(xvecoo)((x-3)/(x+2))^xi se q u a lto` `e` (b) `e^(-1)` (c) `e^(-5)` (d) `e^5`

A

e

B

`e^-1`

C

`e^-5`

D

`e^5`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
` lim_(xto oo) ((x-3)/(x+2))^x = (1+(-5)/(x+2))^x`
` lim_(xto oo) ((x-3)/(x+2))^x = e ^(lim_(xto oo)-(5x)/(x+2))=e^-5[lim_(xto oo)(-5)/(1+(2)/(x)=-5)]`
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