Question

lim x->o (1-cosx)/x sqrt

Answer 1

This seems to be a bit weird sqrt of what?

Answer 2

it's the new way...

Answer 3

lol

Answer 4

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

Answer 5

the lower is
x^2

Answer 6

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

Answer 7

yes yes

Answer 8

do you l'hospital?

Answer 9

i mean know?

Answer 10

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

Answer 11

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

Answer 12

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?

Answer 13

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

Answer 14

the answer should be?

Answer 15

so you got this right ?

Answer 16

actually no. what technique is this?

Answer 17

you wanted to use algebra and limit laws...

Answer 18

do you have any questions with the steps i performed?

Answer 19

is the ans 1/2?

Answer 20

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

Answer 21

1

Answer 22

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

Answer 23

thank you