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Q.

For the curve y sin x = x + y, the equation of the tangent at x = 0 is

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a

2x + y = 0

b

x + y = 0

c

x–y = 0

d

x + 2y = 0

answer is D.

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Detailed Solution

The given curve is y sinx=x+y

Differentiate both sides with respect to x

dydxsinx+ycosx=1+dydxdydx1-sinx=ycosx-1dydx=ycosx-11-sinx

The slope of the tangent to the curve at x=0 is m=dydxat x=0, means at origin.

Hence, m=-1+01=-1

Equation of tangent is y-y1=mx-x1
y-0=-1x-0x-y=0

Therefore, the equation of tangent to the curve y sinx=x+y at x=0 is x+y=0

 

 

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