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Question

f(x)=⎪ ⎪⎪ ⎪sin3(3)log(1+3x)(tan1x)2(e5x1)x,x0a,x=0 continuous in [0,1], if a equals to

A
0
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B
35
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C
2
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D
53
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Solution

The correct option is C 35
We have, f(x)=⎪ ⎪⎪ ⎪sin3(3)log(1+3x)(tan1x)2(e5x1)x,x0a,x=0
For continuity in [0,1],f(0)=f(0+), otherwise it is discontinuous.
Therefore, limx0+sin3(x)log(1+3x)x(tan1x)2(e5x1)
=limx0+[35sin3x(x)3(x)2(tan1x)2×log(1+3x)3x5xe5x1]
=35limx0+sin3x(x)3(x)2tan1x×log(1+3x)3x5xe5x1=a
a=35.

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