Home
Class 12
MATHS
Let {:(f(x)=0," ""when"xlt0),(=1+sin...

Let `{:(f(x)=0," ""when"xlt0),(=1+sinx," ""when"xge0):}`
Show that f'(0) does not exist.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for competitive Exams ( A Mulitple Correct Answers type )|5 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for competitive Exams ( B Integer Answer Type )|4 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Short AnswerType Questions|63 Videos
  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

f(x)={{:(" "2,"when "xlt0),(2+sinx,"when "xge0):} Show that f (x) is continuous at x = 0 but f ' (0) does not exist.

A function f (x) is defined as follows: f(x)={{:(x+2,"when "xlt2),(x^(2)-1,"when "xge2):} Show that f (x) is discontinuous at x = 2 and the jump of the function at this point is -1 .

If f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):} examine whether f(x) is continuous at x = 0.

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

If {:(f(x)=1+x," ""when"x ne 1),(=1," ""when"0lexle1),(2x^(2)+4x+5, " ""when"xgt1):} find f'(x) for real x . Does lim_(x to 0) f'(x) exist ?

A function f(x) is defined as follows : f(x)=x," when "x gt0 =-x," when "x lt0 =-1," when "x=0 Sketch the graph of f(x) and from the graph examine its continuity at x = 0.

A function f (x) is defined as follwos : f(x) {:(=1,","" when " xne0),(=0,","" when " x=0):} Does underset(xrarr0)"lim"f(x) exist ?

CHHAYA PUBLICATION-DIFFERENTIATION-Long Answer Type Questions
  1. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  2. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  3. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  4. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  5. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  6. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  7. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  8. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  9. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  10. Find from the first principle, the derivatives of the following functi...

    Text Solution

    |

  11. Let {:(f(x)=5x-4," ""when "0ltxle1),(=4x^(2)-3x," ""when "xgt1)...

    Text Solution

    |

  12. Let {:(f(x)=0," ""when"xlt0),(=1+sinx," ""when"xge0):} Sh...

    Text Solution

    |

  13. Examine the differentiability of f(x) =2x+|x-1| at x = 1

    Text Solution

    |

  14. Examine the differentiability of f(x) =2x+|x-1| at x = 1

    Text Solution

    |

  15. Given {:(f(x)=x^(2)-2x+3," ""when "xlt1),(=2," ""when "x=1),(=2x...

    Text Solution

    |

  16. If f(x)=sqrt(2x)-sqrt(2/(x))-sqrt(2/(x))+(x+4)/(4-x) find f'(2).

    Text Solution

    |

  17. If 2f(x) +3f(-x)=x^(2)-x+1 then determine the value of f'(1).

    Text Solution

    |

  18. Using the formula of differentiation of product functions show that (d...

    Text Solution

    |

  19. From the relation 1+x+x^(2)+* * * + x^(n-1)=(1-x^(n))/(1-x) , find t...

    Text Solution

    |

  20. If x in(0,(pi)/(2))cup((pi)/(2),pi) and y = sqrt((1-cos 2x)/(1+cos2x...

    Text Solution

    |