Home
Class 12
MATHS
Let f: R->R be a differentiable funct...

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 _______

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • JEE MOCK TEST 13

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

  • JEE MOCK TEST 15

    NTA MOCK TESTS|Exercise MCQS (MATH)|25 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y in R. Then,the value of (log)_(e)(f(4)) is

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

Let f(x) be a differentiable function satisfying the condition f((x)/(y)) = (f(x))/(f(y)) , where y != 0, f(y) != 0 for all x,y y in R and f'(1) = 2 The value of underset(-1)overset(1)(int) f(x) dx is

Find function f(x) which is differentiable and satisfy the relation f(x+y)=f(x)+f(y)+(e^(x)-1)(e^(y)-1)AA x, y in R, and f'(0)=2.

A function f:R rarr R satisfy the equation f(x)f(y)-f(xy)=x+y for all x,y in R and f(y)>0, then

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

" A function "f:R rarr R" satisfies the equation "f(x)f(y)-f(xy)=x+y" and "f(y)>0" ,then "f(x)f^(-1)(x)=

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

NTA MOCK TESTS-JEE MOCK TEST 14-MATHEMATICS
  1. The range of value of alpha such that (0,alpha) lies on or inside the ...

    Text Solution

    |

  2. The value of int(0)^(pi)(Sigma(r=0)^(3)a(r)cos^(3-r)x sin^(r)x)dx depe...

    Text Solution

    |

  3. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

    Text Solution

    |

  4. The sum of 0.2 +0.22+0.222+ … to n terms is equal to

    Text Solution

    |

  5. If tangent at (1, 2) to the circle C1: x^2+y^2= 5 intersects the circl...

    Text Solution

    |

  6. The minimum distance of a point on the curve y=x^2-4 from origin ,

    Text Solution

    |

  7. The domain of the function f(x)=sqrt("ln"((|x|-1))(x^(2)+4x+4)) is

    Text Solution

    |

  8. The expression (1 + tan x + tan^2 x)(1-cot x + cot^2 x) has the positi...

    Text Solution

    |

  9. the value of theta for which the system of equations (sin 3theta)x-2y+...

    Text Solution

    |

  10. If both the mean and the standard deviation of 50 observatios x(1), x(...

    Text Solution

    |

  11. For an initial screening of an admission test, a candidate is given f...

    Text Solution

    |

  12. Let S be the set of all real numbers. Then the relation R= {(a,b):1+...

    Text Solution

    |

  13. The contrapositive of (p vv q)to r is

    Text Solution

    |

  14. (1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8)) is...

    Text Solution

    |

  15. The area of the closed region bounded by y=sec^(-1)x, y ="cosec"^(-1)x...

    Text Solution

    |

  16. Tangents are drawn from the point (alpha, 2) to the hyperbola 3x^2 - 2...

    Text Solution

    |

  17. Let f: R->R be a differentiable function with f(0)=1 and satisfy...

    Text Solution

    |

  18. Let veca, vecb, vecc be three non-zero non coplanar vectors and vecp, ...

    Text Solution

    |

  19. If a complex number z lie on a circle of radius (1)/(2) units, then th...

    Text Solution

    |

  20. int[sin(101 x)*sin^(99)x]dx

    Text Solution

    |