UPSEE Solved Model Paper 3

We have, Lf'(0) =

lim

h→∞

f(0−h)−f(0)

−h

=

lim

h→∞

[tan2(−h)]−(0)

−h

=

lim

h→∞

[tan2h]

−h

= 0
Rf' (0) =

lim

h→∞

f(0+h)−f(0)

h

=

lim

h→∞

[tan2h]−0

h

= 0
∴ Lf' (0) = Rf' (0)
Hence, f (x) is differentiable and hence continuous at a = x , then f' (0) = 0.