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

Answer 1

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

Answer 2

ok I'll try that and see what happens

Answer 3

got it?

Answer 4

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

Answer 5

your denominator isn't correct. check it again carefully

Answer 6

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

Answer 7

no ...

Answer 8

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

Answer 9

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

Answer 10

Oh! I distributed the \[1/x^2\] wrong

Answer 11

Thanks a lot!

Answer 12

so what's the answer?

Answer 13

3/4 I think

Answer 14

Yes, that's right.

Answer 15

Thanks for helping me :)