Ask Me Help Desk - Prove the Continuity and the Differentiable of the Function

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Prove the Continuity and the Differentiable of the Function

Prove that this Function are Continuity and the Differentiable in the Section (-pi,pi).

LINK TO THE Function http://img2.timg.co.il/forums/1_147322584.jpg

Try here if not work in the First link: http://img2.timg.co.il/forums/1_147322584.jpg
Really thank u.

To prove cos(x) is continuous, we can start with

$\lim_{h\to 0}cos(c+h)=\lim_{h\to 0}\left[cos(c)cos(h)-sin(c)sin(h)\right]=cos(c)\lim_{h\to 0}cos(x)-sin(c)\lim_{h\to 0}sin(h)=cos(c)(1)-sin(c)(0)=cos(c)$

Therefore, cos(x) is continuous everywhere.

$cos^{2}(x)$ is also continuous everywhere.

hi thanks about your answer but how I prove that the Function are Differentiable in the Section (-pi,pi)?

there is problem when x=0 no?

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