Find the value

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 $n$.

 

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