Τρίτη, 19 Σεπτεμβρίου 2017

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?          
Πηγή                                              

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