LimitsHard
Question
f(x) = (sin-1x)2. cos (1/x) if x ≠ 0; f(0) = 0, f(x) is :
Options
A.continuous no where in -1 ≤ x ≤ 1
B.continuous everywhere in -1 ≤ x ≤ 1
C.differentiable no where in -1 ≤ x ≤ 1
D.differentiable everywhere in -1 < x < 1
Solution
y = f{x} = 
f(x) can be discontinuous only at x = 0 in [-1, 1]
So we check only at x = 0
LHD (x = 0) =
= -1. 0. [finite quantity between [-1,1]] = 0
RHD (x = 0) is
Hence f(x) is differentiable as well as continuous in [-1,1]
f(x) can be discontinuous only at x = 0 in [-1, 1]
So we check only at x = 0
LHD (x = 0) =
= -1. 0. [finite quantity between [-1,1]] = 0RHD (x = 0) is
Hence f(x) is differentiable as well as continuous in [-1,1]
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