lim as x approaches 0 of
(x^2)*(3+sin(x))/((x+sin(x))^2)
I know I'm supposed to use the fact that
lim as x approaches 0 of
sin(x)/x = 1

Question

lim  as x approaches 0 of
(x^2)*(3+sin(x))/((x+sin(x))^2)
I know I'm supposed to use the fact that
lim  as x approaches 0 of
sin(x)/x = 1

jamesj · Answer

Divide top and bottom by x^2.  Then I think you'll see it clearly.

anonymous · Answer

ok I'll try that and see what happens

jamesj · Answer

got it?

anonymous · Answer

I've got  (3+sin(x))/(x+sin(x)/x)^2 but I still can't see how to get the sin(x)/x out of it

jamesj · Answer

your denominator isn't correct.  check it again carefully

anonymous · Answer

isn't (x+sin(x)/x)^2 equal to (x+sin(x))^2/x^2

jamesj · Answer

no ...

anonymous · Answer

should I expand the (x+sin(x))^2?

jamesj · Answer

$$\frac{1}{x^2} (x + \sin x)^2 = \left( x/x + \sin x / x \right)^2 = (1 + \sin x/x)^2$$

anonymous · Answer

Oh! I distributed the $$1/x^2$$ wrong

anonymous · Answer

Thanks a lot!

jamesj · Answer

so what's the answer?

anonymous · Answer

3/4 I think

jamesj · Answer

Yes, that's right.

anonymous · Answer

Thanks for helping me :)