Home
Class 12
MATHS
Let f(x) = {(int0^x abs(1 - t) dt , x gt...

Let `f(x) = {(int_0^x abs(1 - t) dt , x gt 1),(x - 1/2 , x le 1):}`
Then

A

f(x) is continuous at x = 1

B

f(x) is not continuous at x = 1

C

f(x) is differentiable x = 1

D

f(x) is not differentiable x = 1

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos

  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = int_(-1)^x abs(x+1) dx then

let f(x)={( int_0^x|1-t|dt, xgt1),(x-1/2, xle1):} then

Let f(x)={{:(int_(0)^(x)|1-t|dt,"where "xgt1),(x-(1)/(2),"where "xle1):} , then

If f(x)=int_0^x(sint)/t dt ,x >0, then

Let f(x) = x(1/(x - 1) + 1/x + 1/(x + 1)), x gt 1 , Then

Let f(x)={(0", if"-1 le x lt 0),(1", if "x =0),(2", if "0 lt x le1):} and let F(x)= int_(-1)^(x) f(t) dt, -1 le x le 1 , then

The function f(x) =int_0^xsqrt(1-t^4) dt is such that

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

Let g(x) =int_0^x f(t) dt where f is such that 1//2lef(t)le1 for tin[0, 1] and 0 lef(t) le1//2 for tin[1, 2] Then the interval in which g(2) lies.

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If I = int0^2 (e^x)^4 (x - alpha) dx = 0, then alpha lies in the inter...

    Text Solution

    |

  2. Suppose M = int0^(pi/2) cosx/(x+2) dx , N = int0^(pi/4) sinxcosx/(x+1)...

    Text Solution

    |

  3. Let f(x) = max{x + absx, x - [x]}, where [x] de notes the greatest int...

    Text Solution

    |

  4. Let f(x) = {(int0^x abs(1 - t) dt , x gt 1),(x - 1/2 , x le 1):} Then

    Text Solution

    |

  5. Statement - 1 : The value of the integral int(pi/6)^(pi/3) dx/(1 + s...

    Text Solution

    |

  6. The value of the integral int-1^+1 { x^2013/(e^absx (x^2 + cos x)) +...

    Text Solution

    |

  7. The value of I = int0^(pi/4) (tan^(n+1)x)dx + 1/2 int0^(pi/2) tan^(n-1...

    Text Solution

    |

  8. The value of the integral int1^2 e^x (loge x + (x+1)/x)dx is

    Text Solution

    |

  9. Let [a] denote the greatest integer which is less than or equal to a. ...

    Text Solution

    |

  10. The value of the integral int (sin x - x cos x)/(x(x + sin x)) dx is e...

    Text Solution

    |

  11. Let F(x) =int0^x (cos t)/(1 + t^2) dt , 0 le x le 2pi. Then

    Text Solution

    |

  12. The value of the integral int(-pi/2)^(pi/2) (x^2 + In(pi + x)/(pi - x)...

    Text Solution

    |

  13. If g(x)=int0^x cos^4t dt, then g(x + pi) equals

    Text Solution

    |

  14. The value of the integral int(pi/6)^(pi/2) ((1 + sin 2x + cos 2x)/(sin...

    Text Solution

    |

  15. The value of the integral int0^(pi/2) 1/(1 + (tanx)^101) dx is equal t...

    Text Solution

    |

  16. The value of the integral int0^(pi/4) (sin x + cos x)/(3 + sin 2x) dx ...

    Text Solution

    |

  17. The value of the integral int-2^2 (1 + 2 sin x) e^absx dx is equal to

    Text Solution

    |

  18. The value of the integral int1^5 [abs(x-3) + abs(1-x)] dx is equal to

    Text Solution

    |

  19. Let [ x ] denote the greatest integer less than or equal to x, then th...

    Text Solution

    |

  20. The value of underset(n rarr infty)(limt) (nl)^(1/n)/n is

    Text Solution

    |