Home
Class 12
MATHS
Show that f(x)=|x| is continuous at x=0...

Show that `f(x)=|x|` is continuous at x=0

Text Solution

Verified by Experts

`f(x)=|x|={:{(x, xge 0),(-x,x lt 0):}`
Now f(0)=0
`R.H.L = underset(xrarr0^+)(limf(x))=underset(hrarr0)(lim)f(0+h)`
`=underset(hrarr0)(lim)h=0`
`L.H.L=underset(xrarr0^-)(lim)f(x)=underset(hrarr0)limf(0-h)`
`=underset(hrarr0)(lim){-(0-h)}=0`
`therefore` R.H.L = f(0)=L.H.L
`therefore` f(x) is constinuous at x=0 Hence proved.
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5a|30 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5b|8 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If f(x) f(x) ={((x^2-9)/(x-3)","" " xne3),(" 6""," " "x = 3"):} then show that f(x) is continuous at x=3.

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

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

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

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

Show that f(x)=cos x is continuous for all values of x.

Show that f(x) = sinx is continuous for all values of x.

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0 .

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Miscellaneous Exercise
  1. Show that f(x)=|x| is continuous at x=0

    Text Solution

    |

  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. y=(5x)^(3cos 2x) then find (dy)/(dx).

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  6. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

    Text Solution

    |

  7. Prove that:cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-s...

    Text Solution

    |

  8. (log x)^(log x),x gt1

    Text Solution

    |

  9. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

    Text Solution

    |

  10. If y=(sinx-cosx)^(sinx-cosx),pi/4<x<(3pi)/4,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  11. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

    Text Solution

    |

  12. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

    Text Solution

    |

  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint)

    Text Solution

    |

  14. If y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , find (dy)/(dx) in each of the ...

    Text Solution

    |

  15. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

  16. "If "(x-a)^(2)+(y-b)^(2)=c^(2), for some cgt0, prove that ([1+((dy)/(d...

    Text Solution

    |

  17. "If "cos y = x cos(a+y)," with "cos a ne pm1," prove that "(dy)/(dx)=(...

    Text Solution

    |

  18. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |