Home
Class 12
MATHS
Let f: RvecR be a continuous and differe...

Let `f: RvecR` be a continuous and differentiable function such that `f^(prime)(0=1` and `f(x+2y)=f(x)+f(2y)+e^(x+2y)(x+2y)-2y e^(2y)+4x yAAx ,y in R ,` then value of `f(1)` is 1 (b) e (c) `e+2` (d) `1-e`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

Let f: RvecR be a continuous and differentiable function such that (f(x^2+1))^(sqrt(x))=5forAAx in (0,oo), then the value of (f((16+y^2)/(y^2)))^(4/(sqrt(y)))fore a c hy in (0,oo) is equal to 5 (b) 25 (c) 125 (d) 625

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 _______

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 _______

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The value of f(4) is

Let 'f' be a fifferentiable real valued function satisfying f (x+2y) =f (x) +f (2y) + 6xy (x+2y) AA x, y in R. Then f ' (0), f" (1), f'(2)….. are in

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

Let f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0 and f(0)=0 then the value of f(1) +f(2)=

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f(9) is

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Exactly two real roots, when k belongs to

    Text Solution

    |

  2. The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, )...

    Text Solution

    |

  3. Let f: RvecR be a continuous and differentiable function such that f^(...

    Text Solution

    |

  4. If A is a square matrix of order 3 such that |A|=2, then |("adj "A^(-1...

    Text Solution

    |

  5. The coefficient of the term independent of x in the expansion of (sqrt...

    Text Solution

    |

  6. If (1+x-2x^2)^6=1+a1x+a2x^(2)++a(12)x^(12), then find the value of a2+...

    Text Solution

    |

  7. If the line x-1=0 is the directrix of the parabola y^(2)-kx+8=0, then ...

    Text Solution

    |

  8. Consider lim(x->0)(a x+b e^(-x)+sinx+1)/(a x-bsinx)=l(l is finite) the...

    Text Solution

    |

  9. The value f the integral int(-pi)^pisinm xsinn xdx , for m!=n(m , n in...

    Text Solution

    |

  10. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

    Text Solution

    |

  11. Four persons are selected at random out of 3 men, 2 women and 4 chi...

    Text Solution

    |

  12. If A and B are acute positive angles satisfying the equations 3 sin^(2...

    Text Solution

    |

  13. The equation of the plane through the intersection of the planes x+y+z...

    Text Solution

    |

  14. The position vectors of the points Pa n dQ with respect to the orig...

    Text Solution

    |

  15. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

    Text Solution

    |

  16. Let f(x+y) = f(x). F(y) for all x and y. Suppose f(5) = 2 and f'(0) = ...

    Text Solution

    |

  17. intx^(51)(tan^(- 1)x+cot^(- 1)x)dx=

    Text Solution

    |

  18. General solution of differential equation x^(2)(x+y(dy)/(dx))+(x(dy)/(...

    Text Solution

    |

  19. Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and...

    Text Solution

    |

  20. A bag contains 6 red and 5 blue balls and another bag contains 5 red ...

    Text Solution

    |