will d following function be differentiable at x = 0 ???

1. cos(|x|)+|x|

2. sin(|x|)-|x|

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- Aug 10th 2009, 03:29 PMgaurav1292check d differentiability
will d following function be differentiable at x = 0 ???

1. cos(|x|)+|x|

2. sin(|x|)-|x| - Aug 10th 2009, 04:08 PMTwig
Hi

First one:

If approaches zero from the right, we have:

Now we approach from the left. Note that , is an even function.

So the function is not differentiable at .

The second one you basically do the same thing.

and

.

So the second one is differentiable.