Home
Class 12
MATHS
f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if ...

`f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if x =0):}` at `x = 0` .

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, `f(x)={{:(|x|cos'1/x, if x ne 0),(0, if x =0):}` at `x = 0` .
At `x = 0`, `LHL = underset(xrarr0^(-))(lim)|x|cos'1/x=underset(hrarr0)(lim)|0-h|cos'(1)/(0-h)`
`= underset(hrarr0)(lim)h cos((-1)/(h))`
`= 0 xx `[an oscillating number between `-1` and `1`] =0
`RHL = underset(xrarr0^(+))lim|x| cos'1/x`
`= underset(hrarr0)lim|0+h|cos'(1)/((0+h))`
`= 0x` [an oscillating number between `-1` and `1`] = 0
and `f(0) = 0`
Since, `LHL = RHL = f(0)`
Since, `LHL = RHL = f(0)`
So, `f(x)` is continuous at `x = 0`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

f(x) = {{:(x^(2)sin'1/x, if x ne 0),(0, if x = 0):} at x = 0 .

f(x) = {{:(|x|sin\ (1)/(x-a),if x ne 0),(0, if x =a):} at x = a

f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0 .

Examine the continuity of the following function at the indicated pionts. f(x)={{:(,x^(2) cos (1/x) , x ne 0),(,0 , x =0):}" at x=0"

f(x) = {{:((1-cosAx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):}at x = 0

NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. f(x) = {{:((2x^(2)-3x-2)/(x-2), if x ne 2), (5, if x = 2):} at x = 2.

    Text Solution

    |

  2. f(x)= {{:((|x-4|)/(2(x-4)), if x ne 4),(0,if x = 4):} at x = 4.

    Text Solution

    |

  3. f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if x =0):} at x = 0 .

    Text Solution

    |

  4. f(x) = {{:(|x|sin\ (1)/(x-a),if x ne 0),(0, if x =a):} at x = a

    Text Solution

    |

  5. f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):} at x = 0

    Text Solution

    |

  6. {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):} at x = ...

    Text Solution

    |

  7. f(x) = |x| + |x-1| at x = 1.

    Text Solution

    |

  8. f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

    Text Solution

    |

  9. If f(x)={(2^(x+2)-16)/(4^x-16),ifx!=2k ,ifx=2i scon t inuou sa tx=2,f...

    Text Solution

    |

  10. f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1),...

    Text Solution

    |

  11. f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

    Text Solution

    |

  12. Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if ...

    Text Solution

    |

  13. Find the values of a and b sucht that the function f defined by ...

    Text Solution

    |

  14. If the function f(x) = 1/(x+2), then find the points of discountinu...

    Text Solution

    |

  15. Find all point of discountinuity of the function f(t) = (1)/(t^(2)...

    Text Solution

    |

  16. Show that the function f(x) = |sinx+cosx| is continuous at x = p...

    Text Solution

    |

  17. Examine the differentiability of f, where f is defined by f(x) =...

    Text Solution

    |

  18. f(x) = {{:(x^(2)sin'1/x, if x ne 0),(0, if x = 0):} at x = 0.

    Text Solution

    |

  19. f(x)={{:(1+x, if x le 2),(5-x,ifx gt 2):} at x = 2.

    Text Solution

    |

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

    Text Solution

    |