Home
Class 11
MATHS
f^(prime)(x)=phi(x) and phi^(prime)(x)=f...

`f^(prime)(x)=phi(x)` and `phi^(prime)(x)=f(x)` for all x. Also,`f(3)=5` and `f^(prime)(3)=4`. Then the value of `[f(10)]^2-[phi(10)]^2` is _____

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(prime)(3)=4. Then the value of [f(10)]^2 - [ varphi(10)]^2 is _____

f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(prime)(3)=4. Then the value of [f(10)]^2 − [ϕ(10)]^2is _____

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,and f(0)=3, and if f(3)=3, then the value of f(-3) is ______________

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x)for a l lx ,a n df(0)=3,a n dif f(3)=3, then the value of f(-3) is ______________

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,f(0)=3,f(pi/2)=5 . Find f(x).

If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime)(x)fora l lx ,a n df(0)=3,a n diff(3)=3, then the value of f(-3) is ______________

If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=5 , find f(x) .

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

    Text Solution

    |

  2. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  3. f^(prime)(x)=phi(x) and phi^(prime)(x)=f(x) for all x. Also,f(3)=5 and...

    Text Solution

    |

  4. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

    Text Solution

    |

  5. Each question contains statements given in two columns which have t...

    Text Solution

    |

  6. Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)d...

    Text Solution

    |

  7. If for some differentiable function f(alpha)=0a n df^(prime)(alpha)=0,...

    Text Solution

    |

  8. Statement 1: If differentiable function f(x) satisfies the relation f(...

    Text Solution

    |

  9. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

    Text Solution

    |

  10. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),f...

    Text Solution

    |

  11. dy/dx=(sqrt((1-sin2x)/(1+sin2x))) is equal to, 0ltxltpi/2

    Text Solution

    |

  12. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a)(n y)/(sqrt(x^2+a^2...

    Text Solution

    |

  13. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

    Text Solution

    |

  14. (d)/(dx)cos^(-1)sqrt(cosx),0ltxlt(pi)/(2) is equal to

    Text Solution

    |

  15. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |

  16. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

    Text Solution

    |

  17. If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is eq...

    Text Solution

    |

  18. If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a (a)function of x (...

    Text Solution

    |

  19. If y=(log)(sinx)(tanx),t h e n(((dy)/(dx)))(pi/4)"is equal to" (a)4...

    Text Solution

    |

  20. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a)...

    Text Solution

    |