Home
Class 12
MATHS
Show that f(x) = |x-3|, x in R is contin...

Show that f(x) = |x-3|, x in R` is continuous but not differentiable at x =3.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

Similar Questions

Explore conceptually related problems

Show that fx) = x-|x|, x in R is continuous at x=0

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

Show that |x-5| is continuous but not differentiable at x =5.

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

Show that f(x) = {:{(|2x-3|[x],xge1),(sin((pix)/(2)), x <1):} is continuous but not differentiable at x =1.

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. For what values of 'a' and 'b' the function: f(x) = {:{(x^2,xlec),(a...

    Text Solution

    |

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

    Text Solution

    |

  3. Show that f(x) = |x-3|, x in R is continuous but not differentiable at...

    Text Solution

    |

  4. Write an example of a function, which is continuous everywhere but fai...

    Text Solution

    |

  5. Use Chain Rule to find the derivatives of the following: f(x) = (1-2...

    Text Solution

    |

  6. Find the derivatives of the following: f(x) =(x^2+3x+4).

    Text Solution

    |

  7. Use Chain Rule to find the derivatives of the following: f(x) = (3x^...

    Text Solution

    |

  8. Use Chain Rule to find the derivatives of the following: f(x)=(2x^2+...

    Text Solution

    |

  9. Use Chain Rule to find the derivatives of the following: f(x)=3/(2-x...

    Text Solution

    |

  10. Find the derivatives of the following: h(x) = (x+1)(x+2)(x+3)

    Text Solution

    |

  11. Use Chain Rule to find dy/dx, if y = ((3x-1)/(3x+1)^2)

    Text Solution

    |

  12. Find dy/dx, if y = (4x^3 - 5x^2+1)^

    Text Solution

    |

  13. Find dy/dx, if y = 1-2((5x)/(3x+2))^2 +((5x)/(3x+2))^3

    Text Solution

    |

  14. Differentiate the following w.r.t. x: sin(x^2)

    Text Solution

    |

  15. Differentiate the following w.r.t. x: sin(x^2+5)

    Text Solution

    |

  16. Differentiate the following w.r.t. x: tan(3x+5)

    Text Solution

    |

  17. Differentiate the following w.r.t. x: sinx^0

    Text Solution

    |

  18. Differentiate the following w.r.t. x: sin^4(ax+b)^2

    Text Solution

    |

  19. Differentiate the following w.r.t. x: sin(cotx)

    Text Solution

    |

  20. Differentiate the following w.r.t. x: sin^2(x^5)

    Text Solution

    |