1. ## limit with function

hi
im having trouble with this limit
ill try my best to display it
its the function of sin(x-1) over the quadratic x^2 + x - 2
as x approaches 1

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

2. Originally Posted by chrisc
hi
im having trouble with this limit
ill try my best to display it
its the function of sin(x-1) over the quadratic x^2 + x - 2
as x approaches 1

lim sin(x-1)
x->1 x^2+x-2
Please don't double post. See rule #1 here.

-Dan

3. before you replied, i already edited my first post and apologized for posting in the wrong section. i didnt look at the specific categories for posting. but i thought I would get better luck posting here then just leaving my question in the elementary tab

4. Originally Posted by chrisc
lim sin(x-1)
x->1 x^2+x-2
Well I dunno if someone already helped you, but this is simple, take a look

$\displaystyle \lim_{x\to1}\frac{\sin(x-1)}{(x-1)(x+2)}$

Now define $\displaystyle u=x-1,$ you'll see a well-known limit.

5. If you want to take the easy route, you can always use L'Hopital's rule:

$\displaystyle \lim_{x\rightarrow{1}}\frac{sin(x-1)}{x^{2}+x-2}$

Apply the rule by taking derivative of num and den:

$\displaystyle \lim_{x\rightarrow{1}}\frac{cos(x-1)}{2x+1}$

Now, plug in 1 and what's the limit?.

6. Originally Posted by Krizalid
Well I dunno if someone already helped you, but this is simple, take a look

$\displaystyle \lim_{x\to1}\frac{\sin(x-1)}{(x-1)(x+2)}$

Now define $\displaystyle u=x-1,$ you'll see a well-known limit.
thanks a lot (to the both of ya)
i did the top method, but i had a feeling that this wasn't acceptable (sine being a function)