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Question

Let f(x)=72x9x8x+121+cosx;x0klog2log3;x=0. If f is continuous function at x=0, then k=

A
122
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B
24
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C
182
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D
242
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Solution

The correct option is D 242
Given function is f(x)=72x9x8x+121+cosx;x0klog2log3;x=0
f is continuous at x=0
limx0f(x)=f(0)

limx072x9x8x+121+cosx=f(0)

limx09x(8x1)1(8x1)21+cosx×2+1+cosx2+1+cosx=f(0)

limx0(9x1)(8x1)(2+1+cosx)2(1+cosx)=f(0)

limx0(9x1)x×(8x1)x×x21cosx(2+1+cosx)=f(0)

log9log8.2(2+2)=klog2log3


2log3×3log2×2(2+2)=klog2log3
242=k
Hence, k=242 is the answer.

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