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Question

If y=tan1(11+x+x2)+tan1(1x2+3x+3)+tan1(1x2+5x+7) + ...... + up to n terms. Then y' (0) is equal to

A
11+n2
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B
n21+n2
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C
n1+n2
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D
None of these
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Solution

The correct option is B n21+n2
y=tan1{11+x(1+x)}+tan1{11+(x+1)(x+2)}+tan1{11+(x+2)(x+3)}+......+tan1{11+(x+n1)(x+n)}=nr=1tan1{11+(x+r1)(x+r)}=nr=1tan1{(x+r)(x+r1)1+(x+r1)(x+r)}=nr=1{tan1(x+r)tan1(x+r1)}=tan1(x+n)tan1xy=11+(x+n)211+x2y(0)=11+n21=n21+n2

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