limit of t^2/1-cos^2t as t approaches zero.

im lost I was going to use cost-1/t=0 but don't know how to get it

Question

limit of t^2/1-cos^2t as t approaches zero.

im lost I was going to use cost-1/t=0 but don't know how to get it

freckles · Answer

$$\lim_{t \rightarrow 0}\frac{t^2}{1-\cos^2(t)}$$

freckles · Answer

so you know 1-cos^2(t)=sin^2(t) right?

freckles · Answer

$$\text{ use the following } \ (g(x))^2=g(x) \cdot g(x) \ \text{ and } \ \lim_{x \rightarrow 0}\frac{\sin(x)}{x}=1$$

freckles · Answer

actually the other way works to ... one sec

freckles · Answer

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

anonymous · Answer

wow ive got to memorize trig identities. one question though how are you able to flip it? like how were you able to bring up sin sin^2?

freckles · Answer

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

freckles · Answer

this limit was proved by squeeze theorem