Home
Class 11
MATHS
Let f:[a,b]rarr[1,infty) be a continuous...

Let `f:[a,b]rarr[1,infty)` be a continuous function and lt `g: RrarrR` be defined as
`g(x)={(0, "if x" le a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):}`
Then

A

g(x) is continuous but not differentiable at a

B

g(x) is differentiable on R

C

g(x) is continuous but no differentiable at b

D

g(x) is continuous and differentiable at either a or b but not both

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be defined as g(x)={(0, "if x" lt a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):} Then a) g(x) is continuous but not differentiable at a b) g(x) is differentiable on R c) g(x) is continuous but nut differentiable at b d) g(x) is continuous and differentiable at either a or b but not both.

Let, f:[a,b]to[1,oo) be a continuous function and let g:RR to RR be defined as g(x)={{:(0,"if "x lta","),(int_(a)^(x)f(t)dt,"if "alexleb),(int_(a)^(b)f(t)dt,"if "x gtb):} Then

Let f be a continuous function on [a ,b]dot Prove that there exists a number x in [a , b] such that int_a^xf(t)dt=int_x^bf(t)dtdot

Let f be an odd continous function which is periodic with priod 2 if g(x) = int_0^x f(t) dt then

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

Let f : R rarr R be a continuous function which satisfies f(x) = int_0^x f(t) dt . Then the value of f(log_e 5) is

Let f: R rarr R be a continuous odd function, which vanishes exactly at one point and f(1)=1/2 . Suppose that F(x)=int_(-1)^xf(t)dt for all x in [-1,2] and G(x)=int_(-1)^x t|f(f(t))|dt for all x in [-1,2] . If lim_(x rarr 1)(F(x))/(G(x))=1/(14) , Then the value of f(1/2) is

Let f(x) = int_2^x f(t^2-3t+2) dt then

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

Let f(x) be a continuous function AAx in R , except at x=0, such that int_0^a f(x)dx , ain R^+ exists. If g(x)=int_x^a(f(t))/t dt , prove that int_0^af(x)dx=int_0^ag(x)dx

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f:RrarrR be such that f(2x-1)=f(x) for all x in R . If f is contin...

    Text Solution

    |

  2. Let fbe any continuously differentiable function on [a,b] and twice di...

    Text Solution

    |

  3. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

  4. Letf:RrarrR and g:RrarrR be respectively given by f(x)=|x|+1 and g(x)=...

    Text Solution

    |

  5. The largest value of the non-negative integer a for which lim(xrarr1){...

    Text Solution

    |

  6. Let f1:RrarrR,f2:[0,infty)rarrR,f3:RrarrRandf4:Rrarr[0,infty) be defin...

    Text Solution

    |

  7. lim(xrarr0)sin(picos^2x)/x^2 is equal to :

    Text Solution

    |

  8. If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i ...

    Text Solution

    |

  9. The function f(x)=tan{pi[x-pi/2]}/(2+[x^2] , where [x] denotes the gre...

    Text Solution

    |

  10. Let f(x) be a differentiable function and f'(4)=5. Then lim(xrarr2)(f...

    Text Solution

    |

  11. The value of lim(xrarr0)(int0^(x^2) cos(t^2)dt)/(xsinx) is

    Text Solution

    |

  12. If lim(xrarr0)(2asinx-sin2x)/tan^3x exists and is equal to 1, then the...

    Text Solution

    |

  13. The function f(x)=a sin |x| +be^|x| is differentiable at x=0 when

    Text Solution

    |

  14. let f(x)={( int0^x|1-t|dt, xgt1),(x-1/2, xle1):} then

    Text Solution

    |

  15. The number of points in (-infty,infty) , for which x^3-xsin x-cos x =0...

    Text Solution

    |

  16. lim(xrarr0)((1-cos2)(3+cos x))/(xtan 4x) is equal to

    Text Solution

    |

  17. The limit of xsin (e^(1//x)) as xrarr0

    Text Solution

    |

  18. Let f(x)={f(x={(x^3-3x+2, xlt2),(x^3-6x^2+9x+2, xge2):} Then

    Text Solution

    |

  19. The limit of sum(n=1)^1000(-1)^n x^n as xrarrinfty

    Text Solution

    |

  20. The limit of [1/x^2+(2013)^x/(e^x-1)-1/(e^x-1)] as xrarr0

    Text Solution

    |