Home
Class 12
MATHS
Show that the function 'f' defined as fo...

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at :
`f(x)={{:(3x-2", "0ltxle1),(2x^(2)-x", "1ltxle2),(5x-4", "xgt2):}`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(c) (SHORT ANSWER TYPE QUESTIONS)|34 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(d) (SHORT ANSWER TYPE QUESTIONS)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))|39 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

Similar Questions

Explore conceptually related problems

Show that the function f defined as follows, is continuous at x=2 , but not differentiable: f(x)={3x-2 2x^2 5x 0 2

Show that the function f defined as follows f(x)={3x-2, 0 2 is continuous at x=2 , but not differentiable thereat.

Show that the function f defined as follows f(x)={3x-2,0 2 is continous at x=2 but not differentiable.

Show that the function f(x)={|2x-3|[x]x 0 is continuous but not differentiable at x=1

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

Verify Rolle's Theorem for the function : f(x)={{:(-4x+5", "0lexle1),(2x-3" , "1ltxle2):}

Let f(x)={{:(5x-4",",0ltxle1),(4x^(3)-3x",",1ltxlt2.):} Find lim_(xrarr1)f(x).

Show that f(x)={[5-x,,x>=2],[x+1,,x<2] is continuous at x = 2 but not differentiable at that point.

If the function f(x) defined as f(x)=-(x^(2))/(x),x 0 is continuous but not differentiable at x=0 then find range of n^(2)

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(b) (LONG ANSWER TYPE QUESTIONS (I))
  1. Examine the derivability of the following functions at the specified p...

    Text Solution

    |

  2. Examine the derivability of the following functions at the specified p...

    Text Solution

    |

  3. Examine the derivability of the following functions at the specified p...

    Text Solution

    |

  4. Examine the derivability of the following functions at the specified p...

    Text Solution

    |

  5. If f(x) is differentiable at x=a, find lim(x->a)(x^2f(a)-a^2f(x))/(x...

    Text Solution

    |

  6. If F(x) = f(ax) and f(ax) is differentiable, then prove that F'(x) = a...

    Text Solution

    |

  7. Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...

    Text Solution

    |

  8. Show that the function defined by f(x)=(3-2x), x lt2 and f(x)=3x-7, x ...

    Text Solution

    |

  9. Discuss continuity f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x =...

    Text Solution

    |

  10. Consider the following in respect of the function f(x)={{:(2+x","xge...

    Text Solution

    |

  11. Show that the function 'f' defined as follows, is continuous at x = 2,...

    Text Solution

    |

  12. The function 'f' defined as : f(x)={{:(x^(2)+3x+a", if "xle1),(bx+c"...

    Text Solution

    |

  13. For what choice of aa n db is the function f(x)={x^2,xlt=c a x+b ,x > ...

    Text Solution

    |

  14. Let f:RtoR (R is the set of real numbers) be defined as follows : f(...

    Text Solution

    |

  15. Show that the function f(x)=|x-3|,\ x in \ |R , is continuous but n...

    Text Solution

    |

  16. Show that f(x) = |x-5| is continuous but not differentiable at x =...

    Text Solution

    |

  17. Write an example of a function which is everywhere continuous but f...

    Text Solution

    |