Question:
Evaluate
$\lim _{x \rightarrow 1}\left(\frac{x^{n}-1}{x-1}\right)$
Solution:
To evaluate:
$\lim _{x \rightarrow 1} \frac{x^{n}-1}{x-1}$
Formula used: We have,
$\frac{x^{m}-y^{m}}{x-y}=m y^{m-1}$
As $\mathrm{x} \rightarrow \mathrm{a}$, we have
$\frac{x^{m}-y^{m}}{x-y}=m y^{m-1}$
$\lim _{x \rightarrow a} \frac{x^{n}-1}{x-1}=n$
Thus, the value of $\lim _{x \rightarrow a} \frac{x^{n}-1}{x-1}$ is $n$.