Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ?(adsbygoogle = window.adsbygoogle || []).push({});

As far as i know, cos(x) and sin(x) is differentiable at all x.

If i try to solve this,

lim h->0 (f(x+h) - f(x))/h

when x=0, and substitute cos|x| for f(x).

lim h->0 (cos|h| - cos|0|)/(h) = 1,

so cos|x| is differentiable at x=0 right ?

And for sin|x| ...if i continue doing the same as my previous try,

lim h->0 (sin|h| - sin|0|)/(h) = limh->0 sin|h|/h = 1 .

So both are differenatiable at x=0 as per my explanation,

but the answer given is in another way.

Can you please let me whether it is correct or not ?

Thanks

Mac

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# Homework Help: Differentiation and continuity

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