Evaluate the given limit

by RoRi

September 2, 2015

Compute

$\lim_{x \to 1} \frac{\sin (x^2 - 1)}{x-1}.$

Here, recalling that $\lim_{x \to 0} \frac{\sin x}{x} = 1$ we rearrange the the given expression into this form,

$\begin{align*} \lim_{x \to 1} \frac{\sin (x^2-1)}{x-1} &= \lim_{x \to 1} \left((x+1) \cdot \frac{\sin (x^2-1)}{(x+1)(x-1)} \right) \\ &= \left( \lim_{x \to 1} (x+1) \right) \left( \lim_{x \to 1} \frac{\sin(x^2-1)}{x^2-1} \right) \\ & = 2 \cdot 1 \\ & = 2. \end{align*}$

Stumbling Robot

Evaluate the given limit

Related

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment): Cancel reply