Home
Class 12
MATHS
If x = 3 tant and y = 3 sec t, then the ...

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

Text Solution

Verified by Experts

The correct Answer is:
6
`x=3tant" "therefore" "y=3sect`
`y^(2)-x^(2)=9`
`2yy'-2x=0`
`y'=(x)/(y)`
`y'=(y-xy')/((y)^(2))`
`y'|_(t=(pi)/(4))=(3tan((pi)/(4)))/(3 sec((pi)/(4)))=(1)/(sqrt2),x=3, y=3sqrt2`
`y''=(3sqrt2-3sqrt2)/(18)=(3)/(18sqrt2)=(1)/(6sqrt2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 1 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS - SECTION 2|5 Videos

  • JEE MAIN REVISION TEST - 30 | JEE -2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISION TEST - 1 | JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS ( SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)/(dx^2) at t=pi/4

If x = 2t^3 and y = 3t^2 , then value of (dy)/(dx) is

If x=3tant and y=3sect then find (d^2y)/(dx^2) at x=(pi)/(4) (a) 3 (b) (1)/(6sqrt2) (c) 1 (d) (1)/(6)

If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^2) and (d^2y)/(dx^2)  at t =pi/4.

If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), find the values of (dy)/(dx) at t=pi/4 and t=pi/3dot

If x=cost(3-2\ cos^2t) and y=sint(3-2sin^2t) find the value of (dy)/(dx) at t=pi/4

If x=cost+logtan(t/2),\ \ y=sint , then find the value of (d^2y)/(dt^2) and (d^2y)/(dx^2) at t=pi/4 .

If x = t^(2) and y = t^(3) , then (d^(2)y)/(dx^(2)) is equal to

If x = t^(2) and y = t^(3) , then (d^(2)y)/(dx^(2)) is equal to

Home
Profile