Home
Class 12
MATHS
Let f be a function such that f(xy) = f(...

Let f be a function such that `f(xy) = f(x).f(y), AA y in R and R(1 + x) = 1 + x(1 + g(x))`. where `lim_(x rarr 0) g(x) = 0`. Find the value of `int_(1)^(2) (f(x))/(f'(x)).(1)/(1+x^(2))dx`

Text Solution

Verified by Experts

The correct Answer is:
`= (1)/(2) [log(5//2)]`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 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

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

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

Let f(x) be a continuous function such that f(0) = 1 and f(x)-f (x/7) = x/7 AA x in R , then f(42) is

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2, then

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

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is

f(x)+f(1-1/x)=1+x for x in R-{0,1}. Find the value of 4f(2).

If f (x) = cos (log_e x) , find the value of : f(x) f(y)-1/2[f(x/y)+f(xy)] .

Let f(x) be a polynominal one-one function such that f(x)f(y)+2=f(x)+f(y)+f(xy), forall x,y in R-{0}, f(1) ne 1, f'(1)=3. Let g(x)=x/4(f(x)+3)-int_(0)^(x)f(x)dx, then

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1 , then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f be a function such that f(xy) = f(x).f(y), AA y in R and R(1 + x...

    Text Solution

    |

  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

    Text Solution

    |

  3. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

    Text Solution

    |

  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

    Text Solution

    |

  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

    Text Solution

    |

  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

    Text Solution

    |

  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

    Text Solution

    |

  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |