Home
Class 12
MATHS
Let f : R rarr R be defined as f(x) = in...

Let `f : R rarr R` be defined as `f(x) = int_(-1)^(e^(x)) (dt)/(1+t^(2)) + int_(1)^(e^(x))(dt)/(1+t^(2))` then

A

`f(x)` is periodic

B

`f(f(x)) = f(x) AA x in R`

C

`f(1) = f'(1) = pi/2`

D

`f(x)` is unbounded

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - I|50 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - II|23 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be defined by f(x)=int_(1)^(3)(dt)/(1+|t-x|)* If int_(1)^(3)f(t)dt=(6log_(e)-k)-(k+1) then k=

If f(x)=int_(0)^(x)(dt)/((f(t))^(2)) and int_(0)^(2)(dt)/((f(t))^(2))=(6)^((1)/(3)) then

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

If f(x)= int_(-1)^(x)|t|dt ,x>=-1 then

Let f(x) = int_(-2)^(x)|t + 1|dt , then

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

the value of int_((1)/(e)rarr tan x)(tdt)/(1+t^(2))+int_((1)/(e)rarr cot x)(dt)/(t*(1+t^(2)))=

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
  1. If I = int(0)^(2x)sin^(2)xdx, then

    Text Solution

    |

  2. Given an even function f defined and integrable everywhere and periodi...

    Text Solution

    |

  3. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

    Text Solution

    |

  4. If a,b in R^(+) then find Lim(nrarroo) sum(k=1)^(n) ( n)/((k+an)(k+bn...

    Text Solution

    |

  5. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

    Text Solution

    |

  6. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

    Text Solution

    |

  7. Let I(n) = int(0)^(1//2)(1)/(sqrt(1-x^(n))) dx where n gt 2, then

    Text Solution

    |

  8. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

    Text Solution

    |

  9. Let f(x) = int(0)^(x)|2t-3|dt, then f is

    Text Solution

    |

  10. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

    Text Solution

    |

  11. Let f(x) be a function satisfying f(x) f(x+2) = 10 AA x in R, then

    Text Solution

    |

  12. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

    Text Solution

    |

  13. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

    Text Solution

    |

  14. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

    Text Solution

    |

  15. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

    Text Solution

    |

  16. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

    Text Solution

    |

  17. Let f(x) is a quadratic expression with positive integral coefficient...

    Text Solution

    |

  18. I(1) = int(0)^(pi)(xsinx)/(1+cos^(2)x)dx, I(2) = int(0)^(pi)(x^(2)sin...

    Text Solution

    |

  19. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

    Text Solution

    |

  20. lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...

    Text Solution

    |