BITSAT 2018 Slot 2 Solved Paper

f(0)=0
For f(x) to be continuous at x=0

lim

x→0

f(x)=0
∴

lim

x→0

xp‌sin‌

1

x

=0
This possible only when p>0 ........ (i)
f′(0)=

lim

h→0

f(h)−f(0)

h

=

lim

h→0

hp‌sin‌ 1 h −0

h

=

lim

h→0

hp−1‌sin‌

1

h

⇒f′(0) will exist only when p>0
∴f(x) will not be differentiable if
p≤1 .........(ii)
From Eqs. (i) and (ii), for f(x) to be not differentiable but continuous at x=0, possible values of p are given by 0<p≤1. Hence option (c) is correct.