a) lim _(x arrow 1)(x^2-1) sin (1)/(x-1)=

Name: a) lim _(x arrow 1)(x^2-1) sin (1)/(x-1)=
Brand: QuestionAI
Rating: 4.6 (359 reviews)

Question

Answer 1

To evaluate the limit \(\lim_{x \rightarrow 1} (x^2 - 1) \sin \frac{1}{x - 1}\), we can use the substitution

. As

,

. Therefore, the limit becomes:

First, let's simplify the expression inside the parentheses:

So the limit becomes:

As

, both

and

approach 0. Therefore, the expression simplifies to:

Thus, the limit is:

Soru