Spot the mistake in Differentiation

Spot the mistake in Differentiation

Question                 Let                                                   find f’(0), if exists.

“Supposed solution”         For x ¹ 0,                          Since    does not exist, (see note below)         \  does not exist.     \ f ’ (0) does not exist.         Anything wrong?

Note         L =  does not exist:                 Choose   , then                  Choose    , then          \ L does not exist since  “limit, if exists, must be unique.”

Solution         ,                         = 0      as

For smart mathematician like you

        For this function f(x) in this question:

        (1) Is f(x) continuous at x = 0?

        (2) Is f ’(x) continuous at x = 0?

        (3)   Does f ”(x) exist?          
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