Home
Class 12
MATHS
Let f(x)=|x|+|x-1|, then (a)f(x) is c...

Let `f(x)=|x|+|x-1|,` then (a)`f(x)` is continuous at `x=0,` as well at `x=1` (b)`f(x)` is continuous at `x=0,` but not at `x=1` (c)`f(x)` is continuous at `x=1,` but not at `x=0` (d)none of these

Text Solution

Verified by Experts

At `x=0`
`lim_(x→0​)f(x)=lim_(x→0)​1−2x=1`
`lim_(x→0+)​f(x)=lim_(x→0)​f(x)=lim​_(x→0)1=1`
It is continuous at 0
At `x=1 lim_(x→1−)​f(x)=1`
...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=|x|+|x-1|, then (a) f(x) is continuous at x=0, as well at x=1( b) f(x) is continuous at x=0, but not x=1(c)f(x) is continuous at x=1, but not at x=0 (d)none of these

Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

The function f(x)=sin^(-1)(cos x) is discontinuous at x=0 (b) continuous at x=0( c) differentiable at x=0 (d) none of these

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

If f(x)={(1)/(1+e^(1/x)),quad x!=00,quad x=0 then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

The function f(x)={(e^((1)/(x))-1)/(e^((1)/(x))+1),x!=00,x=0 (a)is continuous at x=0 (b)is not continuous at x=0( chis not continuous at continuous at be made continuous at x=0 (d) none of these

Let f(x)={[(1-cos4x)/(x^(2)), if x 0 continuous at x=0.

RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. Let f(x)={(x-4)/(|x-4|)+a ,x<4a+b ,(x-4)/(|x-4|)+b ,x >4 Then f(x) is...

    Text Solution

    |

  2. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

    Text Solution

    |

  3. Let f(x)=|x|+|x-1|, then (a)f(x) is continuous at x=0, as well at ...

    Text Solution

    |

  4. Let f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|)\ \ \ \ ,\ \ \ x!=1,\ 1 6\ \ \ \ ...

    Text Solution

    |

  5. If f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b x...

    Text Solution

    |

  6. If f(x)={m x+1\ \ \ ,\ \ \ xlt=pi/2,\ \ \ \ \ \sinx+n\ \ \ ,\ \ \ x >p...

    Text Solution

    |

  7. The value of f(0), so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

    Text Solution

    |

  8. The value of f(0), so that the function f(x)=((27-2x)^(1/3)-3)/(9-3(2...

    Text Solution

    |

  9. The value of f(0) so that the function f(x)=(2-(256-7x)^(1/8))/((5x+32...

    Text Solution

    |

  10. f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is ...

    Text Solution

    |

  11. The function f(x)={x^2a\ \ \ \ \ ,\ \ \ \ \ 0lt=x<1,\ \ \ \ \a ,\ \ \ ...

    Text Solution

    |

  12. If f(x)=(1-sinx)/((pi-2x)^2),w h e nx!=pi/2a n df(pi/2)=lambda, the f(...

    Text Solution

    |

  13. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

    Text Solution

    |

  14. The function f(x)=tanx is discontinuous on the set {npi; n in Z} (b)...

    Text Solution

    |

  15. The function f(x)={(sin3x)/x ,x!=0k/2,x=0 is continuous of x=0,t h e ...

    Text Solution

    |

  16. If the function f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at ea...

    Text Solution

    |

  17. If f(x)=1/(1-x), then the set of points discontinuity of the function ...

    Text Solution

    |

  18. Let f(x)=(tan(pi/4-x))/(cot2x),x!=pi/4 . The value which should be ass...

    Text Solution

    |

  19. The function f(x)=(x^3+x^2-16 x+20)/(x-2) is not defined for x=2. In o...

    Text Solution

    |

  20. If f(x)={asinpi/2(x+1), ,xlt=0(tanx-sinx)/(x^3),x >0 is continuous at...

    Text Solution

    |