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The value of lim(xrarr3) ((x^(3)+27)log(...

The value of `lim_(xrarr3) ((x^(3)+27)log_(e)(x-2))/(x^(2)-9)` is

A

9

B

18

C

27

D

`5//3`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xrarr3)(lim)((x^(3)+27)log_(e)(x-2))/((x^(2)-9))`
`=underset(xrarr3)(lim)((x+3)(x^(2)+9-3x)log_(e)(1+(x-3)))/((x+3)(x-3))`
`=underset(xrarr3)(lim)(x^(2)+9-6x)`
`=18-9=9`
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