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Question

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

A
18
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B
12
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C
14
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D
none of these
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Solution

The correct option is A 18
For the function to be continuous, the value of the function at x=0 must be equal to its limit at this point. So,
f(0)=limx0f(x)=limx01cos(1cosx)x4=limx01cos(2sin2x2)x4=limx02sin2(sin2x2)x4=limx02sin2(sin2x2)(sin2x2)2sin4x2(x2)4116=18

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