Home
Class 12
MATHS
Test the continuity and differentiabilit...

Test the continuity and differentiability at `x=1` of the function f defined by
`f(x)={{:(3^(x)", "-1lexlt1),(4-x", "-1lexlt4):}`

Text Solution

Verified by Experts

The correct Answer is:
Continuous at `x=1` but not differentiable at at `x=1`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (1 MARK)|8 Videos

  • CHSE ODISHA EXAMINATION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|11 Videos

  • DETERMINANTS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE |39 Videos

Similar Questions

Explore conceptually related problems

Examine the differentiability of the function f defined by f(x)={{:(2x+3", if "-3lexlt-2),(x+1", if "-2lexlt0),(x+2", if "0lex le1):}

Write the domain of the function defined by f(x)= sin^(-1)x+cosx

Discuss the continuity and differentiability of function f(x)=|x|+|x-1| in the interval (-1,2).

Examine the following function f(x) for continuity at x=1 and differentiability at x=2 , f(x)={:{(5x-4", if "0ltxlt1),(4x^(2)-3x", if "1lexlt2),(3x+4", if "xge2):}

Examine the continuity of the function f defined by f(x) = {[2x+1if x 1]:} .

Discuss the continuity of the function f, where f is defined by f(x)={:{(-2", if" xle-1),(2x", if "-1ltxle1),(2", if "xgt1):}

Test the differentiability of the following functions f(x)=x/(1+absx)at x=0 .

ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -CHAPTER PRACTICE (4 MARK)
  1. Find the derivative of the function w.r.t. x at x=1, cos^(-1)[sinsqrt(...

    Text Solution

    |

  2. If y=e^(m sin ^(-1)x), then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)...

    Text Solution

    |

  3. Test the continuity and differentiability at x=1 of the function f def...

    Text Solution

    |

  4. Show that the function f(x)=|x-1|+|x-2| is not differentiable at x=2.

    Text Solution

    |

  5. If a function f is differentiable at a point c, then prove that it is ...

    Text Solution

    |

  6. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

    Text Solution

    |

  7. Find the derivative of (x+sinx)/(x+cosx) w.r.t. x.

    Text Solution

    |

  8. Differentiate w.r.t. x, sin^(-1)[(2^(x+1)*3^(x))/(1+(36)^(x))].

    Text Solution

    |

  9. If y=(sin(ax+b))/(cos(cx+d)), the find (dy)/(dx).

    Text Solution

    |

  10. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

    Text Solution

    |

  11. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

    Text Solution

    |

  12. If x=a((1-t^(2))/(1+t^(2))) and y=(2t)/(1-t^(2)), then find (dy)/(dx).

    Text Solution

    |

  13. If x=a(costheta+log"tan"(theta)/(2)) and y=asin theta, then find the v...

    Text Solution

    |

  14. Differentiate x^(xcosx)+(x^(2)+1)/(x^(2)-1) w.r.t. x.

    Text Solution

    |

  15. If y=(sin x - cos x)^((sinx-cosx)),(pi)/(4)ltxlt(3pi)/(4), then find (...

    Text Solution

    |

  16. If log(sqrt(1+x^(2))-x)=ysqrt(1+x^(2)), then show that (1+x^(2))(dy)/(...

    Text Solution

    |

  17. Discuss the continuity of secant.

    Text Solution

    |

  18. Find the set of points, where the function f given by f(x)=|2x-1|sin x...

    Text Solution

    |

  19. If y=e^(x)sinx, then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0,

    Text Solution

    |

  20. Find (dy)/(dx), where y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2).

    Text Solution

    |