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 _____

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

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

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

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 graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(7)=3, then the value of f^(prime)(3) is__________

If f(x)= log_3x and phi(x)=x^2 ,then the value of f{varphi(3)} will be

If for all values of x and y , f(x+y) =f(x) f(y) and f(5) =2, f'(0)=3, then the value of f'(5) is-

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

If phi (x)=f(x)+x f'(x) , then the value of int phi (x) dx is -

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of lim_(x->0)(((dy)/(dz)))/x

If f(x)=xsinx, then find f^(prime)(pi/2)

Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f^(prime_ prime)(x)-2f^(prime)(x)-15f(x)=0 for all xdot Then the value of (|a b|)/3 is ___

CENGAGE PUBLICATION-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 ...

    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. Match the value of x in column II where derivative of the function in ...

    Text Solution

    |

  5. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

    Text Solution

    |

  6. Each question contains statements given in two columns which have to...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

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

    Text Solution

    |

  15. d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a)1/2sqrt(1+s e cx) (b) sq...

    Text Solution

    |

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

    Text Solution

    |

  17. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |