Home
Class 11
MATHS
Let f(x)={{:(0", ""if "xlt0),(x^(2)",...

Let `f(x)={{:(0", ""if "xlt0),(x^(2)", ""if "0lexlt2),(4", ""if "xge2):}`. Graph the function. Show that f(x) continuous on `(-oo,oo)`.

Text Solution

Verified by Experts

The correct Answer is:
It is continuous at x =2 .hence It is continuousin`(-infty,infty)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 9.6|25 Videos

  • DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|58 Videos

  • DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 9.4|28 Videos

  • DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|73 Videos

  • EXAMINATION QUESTION PAPER MARCH 2019

    PREMIERS PUBLISHERS|Exercise PART -IV|4 Videos

Similar Questions

Explore conceptually related problems

A function f is defined as follows : f(x) = {{:(0," for ",x lt 0),(x ," for ",0 le x lt 1),(-x^(2)+4x-2," for ",1lexlt3),(4-x ," for ",xge3):} Is the function continuous ?

For the function f(x)={{:(x+2", "xgt0),(x-2", "xlt0):}

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.

If f(x) ={{:(x+2,xlt0),(-x^(2)-2,0le xlt1),( x, xge1):} then the number of points of discontinuity of |f(x)|is

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) g(f(x)).

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

Let f(x)={(-,1, -2lexlt0),(x^2,-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) (A) not continuous (B) not differential at one point (C) differential at all points (D) not differential at two points

PREMIERS PUBLISHERS-DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY-SOLUTION TO EXERCISE 9.5
  1. Find the points of discontinuity of the function f, where f(x)={{:(s...

    Text Solution

    |

  2. At the given point x(0) discover whether the given function is continu...

    Text Solution

    |

  3. At the given point x(0) discover whether the given function is continu...

    Text Solution

    |

  4. Show that the function {{:((x^(3)-1)/(x-1)", ""if "xne1),(3", ...

    Text Solution

    |

  5. For what value of alpha is this function f(x)={{:((x^(4)-1)/(x-1)", ...

    Text Solution

    |

  6. Let f(x)={{:(0", ""if "xlt0),(x^(2)", ""if "0lexlt2),(4", ""if ...

    Text Solution

    |

  7. If f and g are continuous functions with f(3) = 5 and lim(xto3)[2f(x)-...

    Text Solution

    |

  8. Find the points at which f is discontinuous. At which of these points ...

    Text Solution

    |

  9. Find the points at which f is discontinuous. At which of these points ...

    Text Solution

    |

  10. A function f is defined as follows : f(x) = {{:(0," for ",x lt 0),...

    Text Solution

    |

  11. Which of the following functions f has a removable discontinuity at x=...

    Text Solution

    |

  12. Which of the following functions f has a removable discontinuity at x=...

    Text Solution

    |

  13. Which of the following functions f has a removable discontinuity at x=...

    Text Solution

    |

  14. Find the constant b that makes g continuous on (-oo,oo)" "g(x)={{:(x^(...

    Text Solution

    |

  15. Consider the function f(x)=x"sin"pi/x. What value must we give f(0) in...

    Text Solution

    |

  16. The function f(x)=(x^2 -1)/(x^3 -1) is not defined at x=1.What value m...

    Text Solution

    |

  17. State how continuity is destroyed at x=x0 for each of the following g...

    Text Solution

    |

  18. State how continuity is destroyed at x=x0 for each of the following g...

    Text Solution

    |

  19. State how continuity is destroyed at x=x0 for each of the following g...

    Text Solution

    |

  20. State how continuity is destroyed at x=x0 for each of the following g...

    Text Solution

    |