VITEEE 2018 Solved Paper

For function to be continuous :
f(0 + h) = f(0 - h) = f(0)
f(0 + h) =

lim

h→0

h sin 1/h = 0 × (a finite quantity) = 0
f(0 - h) =

lim

h→0

- h sin (1/-h) = 0 × (a finite quantity) = 0
Also ,

lim

x→0

x sin 1/x = 0 × (a finite quantity)
= 0
⇒ function is continuous at x = 0
For function to be differentiable :
f (0 + h)= f'(0-h)
f ' (0 + h) =

f′(0+h)−f(0)

h

=

lim

h→0

hsin 1 h −0

h

=

lim

h→0

sin (

1

h

)
which does not exist