Home
Class 12
MATHS
Consider f(x)={{:((x^(2))/(|x|)","x!=0),...

Consider `f(x)={{:((x^(2))/(|x|)","x!=0),(0","x=0.):}`

A

`f(x)` is discontinuous everywhere

B

`f(x)` is continuous everywhere

C

`f'(x)` exists in `(-1,-1)`

D

`f'(x)` exists in `(-2,2)`.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise Latest Question from AIEEE/JEE Examinations|7 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise RCQs (Questions from Karnataka CET & COMED)|25 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise RCQs (Questions from Karnataka CET & COMED)|25 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Recent competitive Questions|12 Videos

Similar Questions

Explore conceptually related problems

Find lim_(xrarr0)f(x) , where f(x)={{:((x)/(|x|)",", x ne0),(0",",x=0):}

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

Evaluate lim_(xrarr0)f(x)," where "f(x)={{:((|x|)/(x)",",x ne0),(0",",x=0):}

(B) Let f(x)={:{(x^(2)|"cos"pi/x|","x!=0),(" 0 ,"x=0):}x inR , then f is :

If f(x)={{:((3sin pi x)/(5x)", "x !=0),(2K" , " x=0):} is continuous at x=0 , then the value of K is

If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 the function f is

Given f(x) ={{:( ( x)/( |x|)),(2),( xne 0),( x= 0) :} } "find " lim _( xto 0) f(x)

MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -MCQs (LEVEL-II)
  1. At the point x=1, the function : f(x)={{:(x^(3)-1,1ltxltoo),(x-1,-oo...

    Text Solution

    |

  2. If f(x)=underset(-1)overset(x)(int)|t|dt,x ge-1, then :

    Text Solution

    |

  3. Consider f(x)={{:((x^(2))/(|x|)","x!=0),(0","x=0.):}

    Text Solution

    |

  4. There exists a function f(x) satisfying : f(0)=1,f(1)=-(1)/(e),f(x)g...

    Text Solution

    |

  5. If f(a)=2,f'(a)=1,g(a)=-,g'(a)=2, then the value of lim(xtoa)(g(x)f(a)...

    Text Solution

    |

  6. Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x), for ...

    Text Solution

    |

  7. If f(x) is odd differentiable function defined on (-oo,oo), such that ...

    Text Solution

    |

  8. Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x), where g(x) is continuous. ...

    Text Solution

    |

  9. The number of points at which the function : f(x)=|x-0*5|+|x-1|+tanx...

    Text Solution

    |

  10. The derivative of tan^(-1) [(sqrt(1 + x^(2)) - 1)/(x)] with respect to...

    Text Solution

    |

  11. If x=sectheta-costheta,y=sec^(n)theta-cos^(n)theta, then ((dy)/(dx))^(...

    Text Solution

    |

  12. The derivative of sec^(-1)((1)/(2x^(2)-1)) w.r.t. sqrt(1-x^(2)) at x=1...

    Text Solution

    |

  13. The differentiable coefficient of x^(6) w.r.t. x^(3) is :

    Text Solution

    |

  14. If y=(sinx)^cosx, then find (dy)/(dx).

    Text Solution

    |

  15. The function f(x)=(x^(2)-1)|x^(2)-3x+1|+cos(|x|) is not differentiable...

    Text Solution

    |

  16. If y=ce^(x//(x-a)), then 1/y(dy)/(dx) is equal to :

    Text Solution

    |

  17. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

    Text Solution

    |

  18. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

  19. Derivative of (log x)^(4) is

    Text Solution

    |

  20. If x=e^(y+e^(y+ . . . . .. "to "oo)),xgt0, then (dy)/(dx) is :

    Text Solution

    |