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Question

The function f(x)=cos3xcos4xxsin2x for x0, f(0)=74 at x=0, is

A
Continuous
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B
discontinuous
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C
left continuous
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D
right continuous
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Solution

The correct options are
A Continuous
C left continuous
D right continuous
From the trigonometric identity,

cos3xcos4x=2sin(7x2)sin(x2)

limx02sin(7x2)sin(x2)xsin2x

=limx0sin(7x2)7x2×sin(x2)x2×xx×2xsin2x×74

Using the property of limits,

f(0)=74

Hence, the given function is continuous.

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