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If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h...

If `f(x)=2/(x-3),g(x)=(x-3)/(x+4)` , and `h(x)=-(2(2x+1))/(x^2+x-12)` then ` lim_(x->3)[f(x)+g(x)+h(x)]` is

(a) `-2`

(b) `-1`

(c) `-2/7`

(d)`0`

A

1

B

`oo`

C

`sqrt(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`f(x)+g(x)+h(x)=(x^(2)-4x+17-4x-2)/(x^(2)+x-12)`
`=(x^(2)-8x+15)/(x^(2)+x-12)=((x-3)(x-5))/((x-3)(x+4))`
`:. underset(xto3)lim[f(x)+g(x)+h(x)]=underset(xto3)lim((x-3)(x-5))/((x-3)(x+4))=-(2)/(7)`
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