Home
Class 12
MATHS
A function f (x) is defined as follwos :...

A function f (x) is defined as follwos :
` f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):}`
Examine whether `underset(xrarr1)"lim"f(x)` exists or not.

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 (Multiple Choice Type Questions)|20 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 (Very Short Answer Type Questions )|56 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXAMPLE|38 Videos

  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|6 Videos

  • LINEAR DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination(E. Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

A function f (x) is defined as follwos : f(x) {:(=1,","" when " xne0),(=0,","" when " x=0):} Does underset(xrarr0)"lim"f(x) exist ?

A function phi(x) is defined as follows : phi(x){:(= 2," when"xne1),(= 0," when"x=1):} Does underset(xrarr1)"lim"phi(x) exist ? If so , find its value .

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Let f(x){:(=1,",""for "xgt0),(=x^(2),",""for "xle0):} ,discuss whether underset(xrarr0)"lim"f(x) exists or not .

A function F(x) is defined as follows: F(x)={:{(1+2x,"when "xle1),(3-2x,"when "x gt1):} Determine F(0), F(-1.5),F(1), F(2.6) and F(x+2).

underset(xrarr1)"lim"(x-1)/(sqrt(x)-1)= ?

A function f (x) is defined as follows: f(x)={{:(x^(4)-3,"when " xle2),(x^(3)+5,"when "xgt2):} Prove that the function f (x) is continuous at x = 2 .

Draw the graph of y=f(x)=(x^(2))/(x) and from the graph examine whether underset(xrarr0)"lim"f(x) exists or not .

A function f(x) is defined as follows : f(x)=x," when "x lt1 =x+1," when "x gt1 =3/2," when "x=1 Draw the graph of f(x) and examine its continuity at x=(1)/(2)and x=1.

A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.

CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Prove that, underset(x rarr 0)(lim)(5^(x)-4^(x))/(x)=log(e)((5)/(4))

    Text Solution

    |

  2. Evaluate: underset(x rarr 0)(lim)log(1+alphax)/(e^(2x)-1)

    Text Solution

    |

  3. Evaluate : underset(xrarr0)"lim"(e^(ax)-1)/(sinbx)

    Text Solution

    |

  4. Evaluate : underset(xrarr0)"lim"(sinx)/(log(e)(1+x)^(1//4))

    Text Solution

    |

  5. Evaluate : underset(xrarr0)"lim"((e^(x)-1)log(1+x))/(sin^(2)x)

    Text Solution

    |

  6. Evaluate : underset(xrarr0)"lim"(3^(x)-1)/((4+x)^(1//2)-2)

    Text Solution

    |

  7. Evaluate :underset(nrarroo)"lim"(n^(4)-n^(2)+6n+1)/(2n^(4)-5n+4)

    Text Solution

    |

  8. Evaluate :underset(xrarroo)"lim"(sqrt(x^(2)+ax)-x).

    Text Solution

    |

  9. Prove that underset(nrarroo)"lim"(1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))...

    Text Solution

    |

  10. Show that underset(xrarr0)"lim"(xtan2x-2xtanx)/((1-cos2x)^(2))=(1)/(2)

    Text Solution

    |

  11. Examine the existence of the following limits : underset(xrarr2)"li...

    Text Solution

    |

  12. Examine the existence of the following limits : underset(xrarr3)"lim...

    Text Solution

    |

  13. Prove that underset(xrarr0)"lim"(3x+|x|)/(7x-5|x|)does not exist .

    Text Solution

    |

  14. Does underset(xrarra)"lim"f(x)=underset(xrarra)"lim"phi(x) "always imp...

    Text Solution

    |

  15. Examine the existence of the following of limits : underset(xrarr...

    Text Solution

    |

  16. Examine the existence of the following of limits : underset(xrarr0)"l...

    Text Solution

    |

  17. If underset(xrarr0)"lim"(1+x)^(1/x)=e "prove that "underset(xrarr0)"li...

    Text Solution

    |

  18. A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle...

    Text Solution

    |

  19. If f (x)=underset(nrarroo)"lim"(1)/(1+x^(2n)) find f (x) for all real ...

    Text Solution

    |

  20. If alpha and beta are the roots of the equation ax^(2)+bx+c=0 , then ...

    Text Solution

    |