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Evaluate, underset(xto1)"lim"(x^(4)-1)/(...

Evaluate, `underset(xto1)"lim"(x^(4)-1)/(x-1)= underset(xtok)"lim"(x^(3)-k^(3))/(x^(2)-k^(2))` , then find the value of k.

A

`3/2`

B

`4/3`

C

`8/3`

D

`3/8`

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 1)(x^(4)-1)/(x-1) = lim_(x to 1)(x^(3)-k^(3))/(x^(2)-k^(2)) rArr 4(1)^(3) = lim_(x to k)((x-k)(x^(2) +k^(2)+kx))/((x-k)(x+k))`
`rArr 4=3/2 k rArr k=8/3`
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