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Question

The value of f(0) so that the function f(x)=1cos(1cosx)x4 is continuous everywhere is

A
18
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B
12
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C
14
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D
13
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Solution

The correct option is A 18
f(x)=limx0f(x)

limx01cos(1cosx)x4

=limx01cos(1cosx)(1cosx)2×(1cosx)2x4

limx01cos(1cosx)(1cosx)2×limx0(1cosxx2)2

As x0
1cosx0
=lim1cosx01cos(1cosx)(1cosx)2×(12)2
=12×(12)2=18

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