Question

I need help with this problem.
lim (cos(x)-1)/(2x^(2)) as x approaches 0

Answer 1

Would L'hopital work here? @Loser66

Answer 2

We have yet to learn that. So please show how to do it without?

Answer 3

yup

Answer 4

Well.. I'm out of ideas xD
Go for it 66

Answer 5

hehehe neither I. without l' hopital. we need some more steps to solve. Let me try.

Answer 6

as cos approaches 0 it looks like 1 but you are subtracting it by 1 so the numerator looks like 0. The denominator keeps getting smaller as well so its looks like 0. final answer is 0/0

Answer 7

Are you allowed to use this?\[\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1\]If so you can solve without L'Hospital if you multiply the top and bottom of the fraction by (cos x + 1). You'll get a numerator of cos^2 x - 1, which is equal to sin^2 x. Then divide out (sin x)/x twice (which is dividing by one, in this limit). The rest is easy.

Answer 8

Bingo, just a very small mistake at cos^2 x -1 = sin^2 x, it's not that, it's = -sin^2 x,

Answer 9

Thanks for the correction, Winner 66.

Answer 10

Thank you for taking your time in solving and explaining how to solve it Creeksider.

Answer 11

@creeksider I am not Winner, I am Loser. hehehe.... I am a loser on this problem, too. You see,

Answer 12

I'm sorry if I left you out, so.... uhh Loser66? Thank you for taking your time in attempting to solve this problem.

Answer 13

no problem. I am useless here, no need to say sorry, friend