FIND lim (1-cos x )/ x^2 as x approaches 0 using lim (sin x / x)= 1?

Answer 1

Best Answer - Chosen by Asker

lim(x-->0) (1 - cos x) / x^2
= lim(x-->0) [(1 - cos x)(1 + cos x)] / [x^2 (1 + cos x)]
= lim(x-->0) [1 - cos^2(x)] / [x^2 (1 + cos x)]
= lim(x-->0) [sin^2(x)] / [x^2 (1 + cos x)]
= lim(x-->0) [sin x / x]^2 * [1/(1 + cos x)]
= 1^2 * (1/(1 + 1))
= 1/2.

I hope this helps!

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Asker's Comment:

thnx