## anonymous 4 years ago lim x^2cos2x/1-cosx x->0 Can someone explain to me how you solve this?

1. slaaibak

Use L'Hospitals rule. If the limit is in an indeterminate form, the limit of f(x)/g(x) is equal to f'(x)/g'(x)

2. anonymous

I dont think I cant use that they'll mark me off on my test. We can only use calc I stuff.

3. anonymous

im suppose to use something along the lines of lim(h->0) sinh/h=1 or lim(h->0) cosh-1/h=0, I'm guessing because thats what they put in the examples.

4. slaaibak

You should be able to do partition it like that. I'll do it quickly

5. anonymous

the only rule i can see that applies is the quotient rule lim(x->c) f(x)/g(x)= lim f(x)/ lim g(x) if g(x) not equal to zero

6. myininaya

$\frac{x^2 \cos(2x)}{1-\cos(x)}=\frac{x^2 \cos(2x)}{1-\cos(x)} \frac{1+cos(x)}{1+cos(x)}$ $\frac{x^2 \cos(2x) (1+\cos(x))}{1-\cos^2(x)}$ $\frac{x^2 \cos(2x)}{\sin^2(x)}=\frac{x^2}{\sin^2(x)} \cdot \cos(2x) =(\frac{x}{\sin(x)})^2 \cdot \cos(2x)$

7. myininaya

that should help

8. slaaibak

$\lim_{x \rightarrow 0} {x^2 \cos2x \over 1- \cos x} = \lim_{x \rightarrow 0} {x^2 \cos 2x (1+ cosx) \over \sin^2 x}$ Meh too late. What myinanaya said!

9. myininaya

oops i left over my (1+cos(x))

10. myininaya

sorry i'm on my slow laptop

11. anonymous

myininaya is the master of these trig limits

12. anonymous

sin^2x when x=0 is 0 that would make it undefined though

13. anonymous

or even with sinx on the bottom

14. myininaya

$\lim_{x \rightarrow 0}\frac{x}{\sin(x)}=1$

15. slaaibak

I didn't complete mine as myin was before me

16. myininaya

I just left off a factor by the way (1+cos(x)) so don't forget to look at that when you are doing this @ awstin

17. anonymous

makes you appreciate l'hopital

18. anonymous

I get it now thank you, I didnt know that x/sinx = 1 though lol

19. anonymous

l'hopital makes this easier?

20. myininaya

you actually prove that on the way to proving sin(x)/x->1 as x->0 when using squeeze thm

21. anonymous

cacl is hard :\ I was amazing at precalc too!

22. anonymous

calc*