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Differential Calculus

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9 Sep 2007 11:55:19 IST

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A function is defined parametrically by the equations

f(t) = x = 2t+ t² sin1/t if t

0 and 0 if t=0

g(t) = y = 1/t sin t² if t

0 and 0 of t = 0.

find the equation of tangent at point for t= 0 if exist.

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venkat v.t

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Joined: 7 Aug 2007

Posts: 244

9 Sep 2007 13:26:18 IST

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Equation of tangent at t=0 us x-2y=0.

Sol) f¹(0)=

_{[ t]}

_{[ 0]} {2t+t²Sin(1/t)-0}/t =2+0=2

g¹(0)=

_{[ t]}

_{[ 0]} (1/t)Sint²/t =1

Therefore slope of tangent at t=0 to the given curve is g¹(0)/f¹(0)=1/2.

The point of contact is (0,0) {given in the problem}

So by using point-slope form the tangent is x-2y=0.

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