Home
Class 12
MATHS
A derivable function f : R^(+) rarr R sa...

A derivable function `f : R^(+) rarr R` satisfies the condition `f(x) - f(y) ge log((x)/(y)) + x - y, AA x, y in R^(+)`. If g denotes the derivative of f, then the value of the sum `sum_(n=1)^(100) g((1)/(n))` is

A

(a)5050

B

(b)5510

C

(c)5150

D

(d)1550

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

The function f :R -> R satisfies the condition mf(x - 1) + nf(-x) = 2| x | + 1 . If f(-2) = 5 and f(1) = 1 find m and n

Function f : R rarr R f(x) = 3 x -5 is

Let f : R^(+) rarr R satisfies the functional equation f(xy) = e^(xy - x - y) {e^(y) f(x) + e^(x) f(y)}, AA x, y in R^(+) . If f'(1) = e, determine f(x).

Suppose a function f(x) satisfies the following conditions f(x+y) = (f(x) + f(y))/(1+f(x)f(y)), AA x in R, y and f'(0) = "1. Also," -1 The value of the limit l t_(xto oo) (f(x))^(x) is:

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

If f: R rarrR satisfying: f(x-f(y)) = f(f(y) +f(x)-1, for all x, y in R , then -f(10) equals.

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

    Text Solution

    |

  2. Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...

    Text Solution

    |

  3. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  4. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

    Text Solution

    |

  5. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

    Text Solution

    |

  6. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  7. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  8. Find dy/dx if y=2x^7

    Text Solution

    |

  9. if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0 , is continuous at x=0 , t...

    Text Solution

    |

  10. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  11. Let f(x) = {{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  12. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  13. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  14. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  15. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  16. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  17. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  18. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  19. The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not dif...

    Text Solution

    |

  20. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |