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lim(x to (1)/(2))lim (4x^(2)+8x-5)/(1-4x...

`lim_(x to (1)/(2))lim (4x^(2)+8x-5)/(1-4x^(2))=`

A

`-3`

B

`-(1)/(2)`

C

0

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
First factor the numerator and denominator and cance common factors :
`(4x^(2)+8x-5)/(1-4x^(2)=((2x-1)(2x+5))/((1-2x)(1+2x))`
`=(-(1-2x)(2x+5))/((1-2x)(1+2x))`
`= (-(2x+5))/(1+2x)`
`= (-2x-5)/(2x+1)`
Then plug in `x = (1)/(2)` :
`(-2x-5)/(2x+1)=(-2((1)/(2))-5)/(2((1)/(2))+1)`
`= (-1-5)/(1+1)`
`= (-6)/(2)=-3`
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