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Question

If y is an implicit function of x defined by x2x2xxcoty1=0. Then, y(1) is equal to

A
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C
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Solution

The correct option is A 1
x2x2xxcoty1=0. ...............[1]

At x=1; we have

1coty1=0

y=π2

Differentiating w.r.t x, we get:

2x2x(1+lnx)2[xx(cosec2ydydx+cotyxx(1+lnx))]=0

At P(1,π2), we have

2(1+ln1)2[1(1)dydx|P+0]=0

2+2dydx|P=0

dydx|P=1

Hence, y(1)=1

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