Home
Class 12
MATHS
If f(x+y)=f(x)f(y) and f(x)=1+"xg(x) G(...

If `f(x+y)=f(x)f(y)` and `f(x)=1+"xg(x) G(x)"`, where `lim_(xto0)g(x)=a` and `lim_(xto0)" G(x)=b`. Then `f'(x)` is equal to :

A

1+ab

B

ab

C

a/b

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

If lim_(xto0)phi(x)=a^(2),a!=0 , then lim_(xto0)phi(x//a) is equal to

lim_(xto0)(e^(x^(2))-cosx)/(x^(2)) , is equal to

Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :

Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x) , where g(x) is continuous. Then f'(x) is equal to :

Evaluate lim_(xto0)|x|^(sinx)

Let g(x)=1+x-[x] and f(x)={:{(-1","x 0):} Then for all x,f(g(x)) is equal to :

If f(x) = ax+b and g(x) = cx+d then f(g(x)) = g(f(x)) is equivalent to

If f(x) = (2)/(x-3), g(x) = (x-3)/(x+4) and h (x) = (-2(2x + 1))/(x^(2) + x - 12) , then lim_(x rarr 3) [f(x) + g(x) + h(x)] is equal to :

If f(x)=xtan^(-1)x , then lim_(xto1)(f(x)-f(1))/(x-1)=

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x) = {((tanx - cotx)/(x-pi/4), xne pi/4),(a, x = pi/4):}. The va...

    Text Solution

    |

  2. The value of f(0), so that the function f(x) = (sqrt(a^(2)-ax+x^(2))-s...

    Text Solution

    |

  3. The function f(x)=1+|sinx| is :

    Text Solution

    |

  4. The range of the function f(x)=[x]-x , where [x] denotes the greatest ...

    Text Solution

    |

  5. Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^('...

    Text Solution

    |

  6. Let f : R rarr R be a function defined by f(x) = max {x,x^(3)}. The se...

    Text Solution

    |

  7. The domain of the derivative of the function f(x) = {(tan^(-1)x, |x|le...

    Text Solution

    |

  8. lim(h rarr 0) (f(2h+2+h^(2))-f(2))/(f(h-h^(2)+1)-f(1)) given that f^('...

    Text Solution

    |

  9. If f(x) is differentiable increasing function, then lim(x to 0) (f(x^(...

    Text Solution

    |

  10. If f(x) is continuos and differentiable function such that f(1/n) = 0 ...

    Text Solution

    |

  11. Let f(x+y) = f(x).f(y), forall, x, y. Suppose f(5) =2, f^(')(0) = 3 th...

    Text Solution

    |

  12. If f(x) = {(x-5,x le1),(4x^(2)-9, 1ltxlt2),(3x+4, x ge2):} then f^(')(...

    Text Solution

    |

  13. If f(2) = 4 and f^(')(2) =1 then lim(x rarr 2) (x f(2)-2f (x))/(x-2)

    Text Solution

    |

  14. If f(x+y) = 2f(x) f(y) for all x,y where f^(')(0) = 3 and f(4) =2, the...

    Text Solution

    |

  15. If x+4|y| = 6y, then y as a function of x is

    Text Solution

    |

  16. If f(x+y)=f(x)f(y) and f(x)=1+"xg(x) G(x)", where lim(xto0)g(x)=a and...

    Text Solution

    |

  17. The function f(x)=x^(3)-3x is :

    Text Solution

    |

  18. Let f(x)=x(x-sqrt(x+1)). Then :

    Text Solution

    |

  19. It is given that f^(')(a) exists, then lim(x rarr a) (x f(a) - a f(x))...

    Text Solution

    |

  20. Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x), where g(x) is continuous. ...

    Text Solution

    |