Home
Class 12
MATHS
If f(x) = 2^(|x|) where [x] denotes the...

If `f(x) = 2^(|x|)` where `[x]` denotes the fractional part of x. Then which of the following is true ?

A

f is periodic

B

`underset(0)overset(1)int2^([x])dx = 1/(ln2)`

C

`underset(0)overset(1)int2^([x]) dx = log_(2)e`

D

`underset(0)overset(100)int2^([x]) dx = 100 log_(2) e`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
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 defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fractional part of x. Then, which of the following is/are correct?

If f(x)-{x^(2)}-({x})^(2), where (x) denotes the fractional part of x, then

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.

f(x)=min(x^(3),x^(2)) and g(x)=[x]^(2)+sqrt({x}^(2)), where [x] denotes the greatest integer and {x} denotesthe fractional part function.Then which of the following holds?

The range of f(x) =sin(sin^(-1){x}) . where { ·} denotes the fractional part of x, is

If f(x)={x}+sin ax (where {} denotes the fractional part function) is periodic,then

The domain of f(x)=sqrt(x-2{x}). (where {} denotes fractional part of x ) is

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
  1. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

    Text Solution

    |

  17. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

    Text Solution

    |

  18. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,a n dt h ex-a xi sd...

    Text Solution

    |

  19. Let f(x) be a non-negative, continuous and even function such that are...

    Text Solution

    |

  20. Let 'c' be a positive real number such that area bounded by y = 0 , y...

    Text Solution

    |