Question

lim x->1
(sin(x-1))/(x^2+x-2)

I factored the denominator. Now what?

Answer 1

what did you get?

Answer 2

oops

Answer 3

(x+2)(x-1)

Answer 4

shhhh. You didn't see that.

Answer 5

so you got
\[\lim_{x\to 1}\frac{\sin(x-1)}{x-1}\times \frac{1}{x+2}\] first part you should remember and the second is obvious

Answer 6

but it's lim x->1

Answer 7

I thought the identity was only x->0

Answer 8

so?

Answer 9

it is clear to you that as \(x\to 1\) you have \(x-1\to 0\) right?

Answer 10

okay?

Answer 11

in other words,
\[\lim_{x\to 0}\frac{\sin(x)}{x}=\lim_{x\to 1}\frac{\sin(x-1)}{x-1}\] it is just a change of variable

Answer 12

wat. witchcraft.

Answer 13

Okay, then. 1/3

Answer 14

Thanks.

Answer 15

witchcraft for sure, or saying "put \(x-1=y\) " either way
yw