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Question

The equation of the normal to the curve y=2x2+3 sin x at x = 0 is .

A
x + 3y = 0
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B
x - 3y = 0
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C
3x - y = 0
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D
3x + y = 0
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Solution

The correct option is A x + 3y = 0
The equation of the given curve is y=2x2+3 sin x .....[1]
Putting x = 0 in [1], we get y = 0.
So, the point of contact is (0, 0).
Now, y=2x2+3 sin x⇒dydx=4x+3 cos x⇒(dydx)(0, 0)=3.So, the equation of the normal at (0, 0) is y−0=−13(x−0)⇒x+3y=0.

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