## 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?