Home
Class 12
MATHS
If x = cos theta and y = sin^(3) theta, ...

If `x = cos theta and y = sin^(3) theta,` then `|(yd ^(2)y)/(dx ^(2))+((dy)/(dx))^(2)|at theta=(pi)/(2)` is:

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos

  • COMPOUND ANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos

  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If x +y= 3-cos4theta and x-y=4sin2theta then

If x=sin theta and y=cos^(3) then 2y(d^(2)y)/(dx^(2))+4((dy)/(dx))^(2) is

x=acos^(3)theta,y=asin^(3)theta then find (d^(2)y)/(dx^(2))

If x = a cos^(3) theta, y = a sin ^(3) theta then sqrt(1+((dy)/(dx))^(2)) =?

If x=costheta,y=sin5theta," then "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=

If x =2 cos theta - cos 2 theta y = 2 sin theta - sin 2 theta Find (d^(2)y)/(dx^(2)) at theta = pi/2

If x=acos^3theta,y=a sin^3theta then find (d^2y)/(dx^(2))

If x=a(1-cos^3theta) , y=a\ sin^3theta , prove that (d^2y)/(dx^2)=(32)/(27\ a) at theta=pi/6 .

If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))^2=3\ s in^2theta(5\ cos^2theta-1) .

Find dy/dx x=a\ cos^3theta , y=a\ sin^3theta

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

    Text Solution

    |

  2. The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

  3. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  4. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  5. Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...

    Text Solution

    |

  6. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  7. If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...

    Text Solution

    |

  8. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  9. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  10. f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  11. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  12. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  13. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y^('') +xy')/(y)| is equal to

    Text Solution

    |

  14. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  15. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  16. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |

  17. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

    Text Solution

    |

  18. If x = cos theta and y = sin^(3) theta, then |(yd ^(2)y)/(dx ^(2))+((d...

    Text Solution

    |

  19. The value of x, x in (2,oo) where f (x) = sqrt(x sqrt(8x-16))+ sqrt(x-...

    Text Solution

    |

  20. The number of non differentiability of runction f (x) = min (|x| , {x}...

    Text Solution

    |