LimitsHard

Question

Given f(x) = . f(x) is differentiable at x = 1 provided:

Options

A.a = - 1, b = 2
B.a = 1, b = - 2
C.a = - 3, b = 4
D.a = 3, b = - 4

Solution


f(1) = 1
a sgn (x +1) cos2(x - 1) + bx2 = a.1.1 + b
for continuity a + b = 1
LHD (x = 1) is
= 2 + 0 + 2 = 4
RHD (x = 1) is

+ bh + 2b = 2b
f(x) is differentiable at x = 1  if    2b = 4
⇒  b = 2   a = - 1

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