Home
Class 12
MATHS
x= 2 cos t -cos 2t ,y=2 sin t-sin 2t The...

`x= 2 cos t -cos 2t ,y=2 sin t-sin 2t `Then the value of `(d^(2)y)/(dx^(2))`at `t=pi/2`

A

`1//2`

B

`5//2`

C

`-3//2`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
We have `x=2cost-cos2t`
and `y=2sint-sin2t`
`therefore" "(dx)/(dt)=-2sint+2sin2t`
`=-2(sint-sin2t)`
And `(dy)/(dt)=2cos t-2cos 2t`
`=2(cost-cos2t)`
`therefore" "(dy)/(dx)=(cos2t-cost)/(sint-sint)`
`(sint-sin2t)(-2sin 2t+sint)`
`therefore" "(d^(2)y)/(dx^(2))=(-(cos2t-cost)(cost-2 cos 2t))/((sint-sin2t)^(2))xx(dt)/(dx)`
`therefore" "(d^(2)y)/(dx^(2)):|_(t=(pi)/(2))=(1(1)-(-1)(+2))/((1)^(2))xx(1)/(-2(1))`
`=-(3)/(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

Similar Questions

Explore conceptually related problems

If x = 3 tant and y = 3 sec t, then the value of (d^2y)/(dx^2)" at" t=pi/4 is

If x=a (cos t +t sin t)" and "y= a (sin t -t cos t) , find (d^(2)y)/(dx^(2)) .

A curve is represented parametrically by the equations x=f(t)=a^(In(b^t))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R. The value of (d^(2)y)/(dx^(2)) at the point where f(t)=g(t) is

If x =a ( cos t + t sin t), y = a [sin t-t cos t] then find dy/dx .

If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) -(pi+4)/2 (c) -2 (d) none of these

If w=x+2y+z^2and x= cos t , y = sin t, z = t Find (dw)/(dt) .

Let f(t)=|{:(cos t,,t,,1),(2 sin t,,t,,2t),(sin t,,t,,t):}| .Then find lim_(t to 0) (f(t))/(t^(2))

For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi The principal value of cos^(-1) (cos 5t^(2)) is

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

Home
Profile