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Question

limn 113+n3+423+n3++12n is equal to

A
13 loge 3
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B
13 loge 2
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C
13 loge 13
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D

None of these

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Solution

The correct option is B 13 loge 2
Let S=limπ 113+n3+423+n3++12n
=limπ 113+n3+423+n3++n2n3+n3
S=limπnr=1r2r3+n3=limπr2n3(r3n3+1)
=limπnr=1 1n.(rn)2[1+(rn)3]
Applying the formula, we get A=10 x21+x3dx
=1310 3x21+x3dx=13[loge(1+x3)]10=13loge2

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