`lim_(x -> 1) sin(x - 1)/(x^2 + x - 2)` Find the limit.

Textbook Question

Chapter 3, 3.3 - Problem 48 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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kspcr111 | In Training Educator

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`lim_(x -> 1) sin(x - 1)/(x^2 + x - 2)`

`=lim_((x-1) -> 0) sin(x - 1)/((x+2)(x-1))`

let `t= x-1`

so,

`lim_((t) -> 0) sin(t)/((t+3)(t))`

As we know that as `t->0 sin(t) = t` , so

`lim_((t) -> 0) sin(t)/((t+3)(t))`

`= lim_((t) -> 0) 1/(t+3)`

`= 1/3`

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