## najwaischua 3 years ago lim x->o (1-cosx)/x sqrt

1. myininaya

This seems to be a bit weird sqrt of what?

2. dpaInc

it's the new way...

3. FoolForMath

lol

4. Kreshnik

LOL @myininaya I thought It was $\LARGE \lim_{x\to 0}{1-\cos x \over \sqrt x}$

5. najwaischua

the lower is x^2

6. Kreshnik

$\LARGE \lim_{x\to 0}{1- \cos x\over x^2}$ ?

7. najwaischua

yes yes

8. myininaya

do you l'hospital?

9. myininaya

i mean know?

10. najwaischua

yes. but the question say use limit rule. don't use l'opitall's rule

11. najwaischua

i've tried to use factorization. but can't get it

12. myininaya

ok $\lim_{x \rightarrow 0}\frac{1-\cos(x)}{x^2} \cdot \frac{1+\cos(x)}{1+\cos(x)}$ $\lim_{x \rightarrow 0}\frac{1-\cos^2(x)}{x^2(1+\cos(x))}=\lim_{x \rightarrow 0}\frac{\sin^2(x)}{x^2(1+\cos(x))}$ need more help?

13. myininaya

$\lim_{x \rightarrow 0}\frac{\sin(x)}{x} \cdot \lim_{x \rightarrow 0}\frac{\sin(x)}{x} \cdot \lim_{x \rightarrow 0}\frac{1}{1+\cos(x)}$

14. najwaischua

15. myininaya

so you got this right ?

16. najwaischua

actually no. what technique is this?

17. myininaya

you wanted to use algebra and limit laws...

18. myininaya

do you have any questions with the steps i performed?

19. niki

is the ans 1/2?

20. Kreshnik

you're supposed to know this rule: $\lim_{x\to0}{\sin x\over x}= ?$ what should be instead of "?"

21. najwaischua

1

22. Kreshnik

so there's nothing to get confused of :) .. @myininaya solved it, you just had to substitute :)

23. najwaischua

thank you