Home
Class 12
MATHS
If y={:{(x","xgt0),(0","x=0","),(-x","xl...

If `y={:{(x","xgt0),(0","x=0","),(-x","xlt0):}` then at `x=0`, y is

A

not continuous

B

continuous but not differentiable

C

differentiable

D

None of these.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MODERN PUBLICATION|Exercise MCQs (LEVEL-II)|35 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

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

If f(x)={{:(|x|+1",",xlt0),(0",",x=0),(|x|-1",",xgt0):} For what value(s) of a does lim_(xrarra)f(x) exists?

Show the signum function f:RrarrR given by f(x)={(1" if "xgt0),(0" if "x=0 " is"),(-1" if " xlt0):} neither one-one nor onto

The area bounded by the curve y={:{(x^(2)","xlt0),(x","xge0):} and the line y=4 is

The area bounded by the curve : y={{:(x^2,xlt 0),(x,x ge 0):}+ and the line y=4 is :

The area bounded by the curve : y={(x^2,x lt 0),(x,xge0):} and the line y=4 is:

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] , show that F(x) F(y)=F(x+y) .

If f(x) = {((1-cos 4x)/x^(2), x lt 0),(a, x =0),((sqrtx)/(sqrt(16+sqrt(x))-4), xgt 0):} then the value of a for which f(x) is continuous at x = 0 is

MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -RCQs (Questions from Karnataka CET & COMED)
  1. If y={:{(x","xgt0),(0","x=0","),(-x","xlt0):} then at x=0, y is

    Text Solution

    |

  2. If the three function f(x),g(x) and h(x) are such that h(x)=f(x)g(x) a...

    Text Solution

    |

  3. The drivative of e^(ax)cos bx with rexpect to x is re^(ax)cosbx+"tan"^...

    Text Solution

    |

  4. If x=acos^(3)theta and y=asin^(3)theta, then (dy)/(dx)=

    Text Solution

    |

  5. If y=tan^(-1)sqrt(x^(2)-1), then the ratio (d^(2)y)/(dx^(2)):(dy)/(dx)...

    Text Solution

    |

  6. If sqrt(r ) =ae^(thetacotalpha) where a and alpha are real numbers the...

    Text Solution

    |

  7. The derivative of "tan"^(-1)(sinx)/(1+cosx) w.r.t. "tan"^(-1)(cosx)/(1...

    Text Solution

    |

  8. d/(dx)[cos^(2)(cot^(-1)sqrt((2+x)/(2-x)))]

    Text Solution

    |

  9. If f(x)=((sin^(2)x)/(1+cotx))+(cos^(2)x)/(1+tan), then f'((pi)/(4)) is...

    Text Solution

    |

  10. If cos^(-1)((y)/(b))=nlog((x)/(n)), then :

    Text Solution

    |

  11. f(x)=2a-x in -altxlta=3x-2a in a lex. Then which of the following i...

    Text Solution

    |

  12. If x+y=tan^(-1)y" and "(d^(2)y)/(dx^(2))=f(y)(dy)/(dx), then f(y)=

    Text Solution

    |

  13. Let f(x) = cos^(-1) [(1)/(sqrt13) (2 cos x - 3 sin x)]. Then f(0.5) =

    Text Solution

    |

  14. If y=(1+x)(1+x^(2))(1+x^(4)), then (dy)/(dx) at x=1 is :

    Text Solution

    |

  15. If y = (tan^(-1)x)^(2) then show that (x^(2) + 1)^(2) (d^2 y)/(dx^2) +...

    Text Solution

    |

  16. If the function f(x) defined by f(x)=(x^(100))/(100)+(x^(99))/(99)+....

    Text Solution

    |

  17. Which of the following functions is differentiable at x=0. ?

    Text Solution

    |

  18. If x=a(cost+logtant//2),y=asint, then (dy)/(dx)=

    Text Solution

    |

  19. If f(x)=xtan^(-1)x, then lim(xto1)(f(x)-f(1))/(x-1)=

    Text Solution

    |

  20. If f(y)=f(x^(2)+2) and f'(3)=5, then (dy)/(dx) at x=1 is :

    Text Solution

    |

  21. If x = a cos^(3) theta , y = a sin^(3) theta , then 1+((dy)/(dx))^(2)...

    Text Solution

    |