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Question

If m=tanxis the slope of the tangent to the curve ey=1+x2 then


A

tanx>1

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B

tanx<1

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C

-1tanx1

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D

-1tanx1

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Solution

The correct option is C

-1tanx1


Explanation for correct option

We know that slope of a tangent is dydx=m

Given m=tanx

Therefore, dydx=m=tanx

Now, given equation of the curve is ey=1+x2

Now differentiating with respect to x we have

eydydx=2xdydx=2xeydydx=2x1+x2

x-120xRx2-2x+10x2+12x1x2+112x2xx2+11

dydx1tanx1

Hence, option(C) i.e. -1tanx1 is correct


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