Question

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

Answer 1

\[\lim_{x \rightarrow 1} \frac{\sin(x-1)}{(x-1)(x+2)}\] \[\lim_{x \rightarrow 1}\frac{\sin(x-1)}{(x-1)}*\frac{1}{(x+2)}\]

Answer 2

\[\frac{1}{3}\]

Answer 3

is this correct?

Answer 4

nope. as x tends to 1, (x-1)=0
and Sin(x-1)=0
the answer is 0

Answer 5

You should have to use L'Hospital Rule, is very useful, is you have 0/0 or inf/inf, you derivate up and down and evaluate the limit wth the result ¨)

Answer 6

1/3 is indeed the right answer.

Answer 7

we never learned L'hospitals rule...