Home
Class 11
MATHS
Let f(x){:{(2x+3",",xle0),(3(x+1)",",xgt...

Let `f(x){:{(2x+3",",xle0),(3(x+1)",",xgt0.):}`
Find `(i) lim_(xrarr0)f(x)" "(ii)lim_(xrarr1)f(x)`

Text Solution

Verified by Experts

(I) We have
`lim_(xto0^(+))f(x)=lim_(hto0)3(0+h+1)=lim_(hto0)3(h+1)=3.`
`lim_(xto0^(-))f(x)=lim_(hto0)3(0-h+1)=lim_(hto0)3(-h+1)=3.`
`thereforelim_(xto0^(+))(x)=lim_(xto0^(-))f(x)=3.`
Hence, `lim_(xto0)f(x)=3.`
(ii) We have
`limf(x)lim_(hto0)f(1+h)=lim_(hto0)3(1+h+1)=lim_(hto0)3(2+h)=6.`
`lim_(xto1^(-))f(x)=lim_(hto0)f(1-h)=lim_(hto0)3(1-h+1)=lim_(hto0)3(2-h)=6.`
`thereforelim_(xto1^(+))f(x)=lim_(xto1)f(x)=6.`
Hence `lim_(xto1)f(x)=6.`
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27A|40 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27B|72 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27C|15 Videos

  • HYPERBOLA

    RS AGGARWAL|Exercise EXERCISE 24|23 Videos

  • LINEAR INEQUATIONS (IN ONE VARIABLE)

    RS AGGARWAL|Exercise EXERCISE 6B|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim_(xrarr1)f(x).

Let f(x)={:{((|x|)/(x)",",xne0),(0",",x=0.):} Find lim_(xrarr0)f(x).

Let f(x)={{:(5x-4",",0ltxle1),(4x^(3)-3x",",1ltxlt2.):} Find lim_(xrarr1)f(x).

lim_(xrarr0) (sin 3x)/x

If f(x) is defined as f(x)={{:(2x,+,3,x,le 0),(3x,+,3,x,le0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

Let f(x)={{:(1+x^(2)",",0lexle1),(2-x",",xgt1.):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x){{:((x)/(|x|)",",xne0),(0",",x=0):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={{:((|x|)/(x)",",xne0),(2",",x=0.):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={{:(4x-5",",xle2),(x-a",",xgt2.):} If lim_(xrarr2)f(x) exists then find the value of a.

RS AGGARWAL-LIMIT-SOLVED EXAMPLES
  1. Evaluate lim(xrarr0)((x^(3)cotx)/(1-cosx)).

    Text Solution

    |

  2. lim(x->0)(sin3x+7x)/(4x+sin2x)

    Text Solution

    |

  3. Evaluate lim(x-> 0) (tan3x-2x)/(3x- sin^2 x)

    Text Solution

    |

  4. Evaluate lim(xrarr0)(xtan4x)/(1-cos4x).

    Text Solution

    |

  5. Evaluate lim(xrarr0)((1-cosxsqrt(cos2x)))/(x^(2)).

    Text Solution

    |

  6. Evaluate lim(xrarr(pi)/(4))((sinx-cosx))/((x-(pi)/(4))).

    Text Solution

    |

  7. Evaluate lim(xrarr(pi)/(2))(cosx)/(((pi)/(2)-x)).

    Text Solution

    |

  8. Evaluate lim(xrarr(pi)/(6))((sqrt3sinx-cosx))/((x-(pi)/(6))).

    Text Solution

    |

  9. Let f(x){:{(2x+3",",xle0),(3(x+1)",",xgt0.):} Find (i) lim(xrarr0)f(...

    Text Solution

    |

  10. Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim(xrarr1)f...

    Text Solution

    |

  11. Let f(x)={:{((|x|)/(x)",",xne0),(0",",x=0.):} Find lim(xrarr0)f(x).

    Text Solution

    |

  12. Suppose f(x)={(a+bx, x<1), (4, x=1), (b-ax, x>1):} and if lim(xrarr1) ...

    Text Solution

    |

  13. If f(x)={{:(|x|+1,xlt0),(0,x=0) ,(|x|-1,xgt0):} for what value (s) ...

    Text Solution

    |

  14. Let f(x)={{:(mx^(2)+n",",xlt0),(nx+m",",0lexle1),(nx^(3)+m",",xgt1):} ...

    Text Solution

    |

  15. Let a(1),a(2),...,a(n) be fixed real numbers and let f(x)=(x-a(1))(...

    Text Solution

    |

  16. Let f(x)={x}= greater integer less than or eqal to x. For any integer ...

    Text Solution

    |

  17. If is an odd function and underset(xto0)f(x) exists then prove tha...

    Text Solution

    |

  18. If f is an even function, prove that lim(xto0^(-)) (x)=lim(xto0^(+)) ...

    Text Solution

    |

  19. Show that lim(xto0^(-)) ((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

    Text Solution

    |

  20. Show that ("lim")(x->0)x/(|x|) does not exist.

    Text Solution

    |