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Question

Let y be an implicit function of x defined by x2x2xx cot y1=0. Then y(1) equals


A

1

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B

log 2

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C

- log 2

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D

- 1

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Solution

The correct option is D

- 1


x2x2xx cot y1=0
2 cot y=xxxx2 cot y=u1u where u=xx
Differentiating both sides with respect to x, we get
2cosec2y dydx=(1+1u2)dudx
where u=xxlog u=x log x
1ududx=1+log x dudx=xx(1+log x)
We get 2 cosec2y dydx=(1+x2x).xx(1+log x)
dydx=(xx+xx)(1+log x)2(1+cot2y)(i)
Now when x=1,x2x2xx cot y1=0,gives 12 cot y1=0coty=0
From equation (i), at x=1 and coty=0, we get y(1)=(1+1)(1+0)2(1+0)=1


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