Home
Class 12
MATHS
If x=s e ctheta-costhetaa n dy=sec^nthe...

If `x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t` `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

If x=cos e ctheta-sintheta and y=cos e c^ntheta-sin^ntheta, then show that (x^2+4)((dy)/(dx))^2=n^2(y^2+4)dot

If x=cosec theta-sin theta and y=cosec^(n)theta-sin^(n) theta , prove that, (x^(2)+4)((dy)/(dx))^(2)=n^(2)(y^(2)+4) .

If x = sec theta - cos theta, y = sec^n theta - cos^n theta , then show that (x^2 + 4) (dy/dx)^2 = n^2 (y^2 + 4)

x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(n^2(y^2+4))/(x^2+4)

If x=sec theta-cos theta, y =sec^(n)theta-cos^(n) theta and (x^(2)+4)((dy)/(dx))^(2)=k(y^(2)+4) then the value of k is -

(x+2)(dy)/(dx)=4x^(2)y

(dy)/(dx)=e^(x+y)+x^(2)e^(y)

Solve : (dy)/(dx)=e^(y-x)+2

(dy)/(dx)=e^(x-y)+x^(2)e^(-y)

If x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. f(x)={(x^2+e^(1/(2-x)))^(-1), x!=2 k ,x=2 is continuous from right at ...

    Text Solution

    |

  2. The derivative of the function represented parametrically as x=2t=|...

    Text Solution

    |

  3. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

    Text Solution

    |

  4. If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuou...

    Text Solution

    |

  5. Find the set of points where the following functions are discontinuous...

    Text Solution

    |

  6. If t(1+x^(2))=x and x^(2)+t^(2)=y then at x = 2, the value of (dy)/(dx...

    Text Solution

    |

  7. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

    Text Solution

    |

  8. If x+y=3e^2t h e d/(dx)(x^y)=0forx= e^2 b. e^e c. e d. 2e^2

    Text Solution

    |

  9. xy=( x+y )^n and dy/dx = y/x then n=   1 b.  2 c. 3 d. 4

    Text Solution

    |

  10. If f(x)={(sin(pi/2)(x-[x]),x<5),(5(b-1),x=5),((a b^2|x^2-11 x+24|)/(x-...

    Text Solution

    |

  11. If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x ...

    Text Solution

    |

  12. Let f(x)={8^(1/x),x<0a[x],a in R-{0},xgeq0, (where [.] denotes the gr...

    Text Solution

    |

  13. let f(x)=x^3-x^2-3x-1 , g(x)=(x+1)aand h(x)=f(x)/g(x) where h is a rat...

    Text Solution

    |

  14. For which of the following functions f(0) exists such that f(x) is con...

    Text Solution

    |

  15. Determine the values of a so that the funtion is continuous at x=1. f...

    Text Solution

    |

  16. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

    Text Solution

    |

  17. Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-...

    Text Solution

    |

  18. The function f:R→R satisfies f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^...

    Text Solution

    |

  19. The second derivative of a single valued function parametrically re...

    Text Solution

    |

  20. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

    Text Solution

    |