Question:
If $\lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}$, then $k$ is :
Correct Option: , 4
Solution:
$\lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}$
$\Rightarrow \lim _{x \rightarrow 1}(x+1)\left(x^{2}+1\right)=\frac{k^{2}+k^{2}+k^{2}}{2 k}$
$\Rightarrow \mathrm{k}=8 / 3$