Home
Class 12
MATHS
Evaluate lim(xto1) (x^(2)+xlog(e)x-log(e...

Evaluate `lim_(xto1) (x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)`

Text Solution

Verified by Experts

`underset(xto1)lim(x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)" "(0/0"from")`
`=underset(xto1)lim((x-1)(log_(e)x+x+1))/((x+1)(x-1))" "(0/0"from")`
`=underset(xto1)lim(log_(e)x+x+1)/(x+1)`
`=(log_(e)1+1+1)/(1+1)=(0+2)/(2)=1`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.1|10 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(xto-1)(x^(2)-5x+6)/(x-1)

Evaluate : ("lim")_(xvec1)(x^2+x(log)_e x-(log)_e x-1)/((x^2-1)

Evaluate lim_(xto1)(x^(7)-1)/(x^(4)-1)

Evaluate x lim_(xto2) (x-2)/(log_(a)(x-1)).

Evaluate lim_(xto0)(1-cos4x)/(x^(2))

Evaluate lim_(xto0^(+)) (x)^((1)/(log_(e)sinx)).

Evaluate int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx

Evaluate lim_(xto1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1)) if xgt1 .

Evaluate lim_(xto1)(1+(x-1)^(2))/(1+x^(2))

Evaluate lim_(xto1) ((2)/(1-x^(2))-(1)/(1-x)).

CENGAGE-LIMITS-Question Bank
  1. Evaluate lim(xto1) (x^(2)+xlog(e)x-log(e)x-1)/((x^(2))-1)

    Text Solution

    |

  2. If Lim(x rarr 0) (1-cosx)/(e^(ax)-bx-1) exist and is equal to 1, then ...

    Text Solution

    |

  3. If graph of a function f(x) is shown in the adjacent figure, then Lim(...

    Text Solution

    |

  4. Let f(x) =(sec x)^(cosecx) + (cot x)^(sin x). Then the value of Lim(x ...

    Text Solution

    |

  5. Lim(z rarr 0){{max((sin^(-1)x + cos^(-1)x)^(2), min(x^(2)+4x+7))}. (si...

    Text Solution

    |

  6. The reciprocal of the value of: ("lim")(ntooo)(1-1/(2^2))(1-1/(3^2))(1...

    Text Solution

    |

  7. The value of Lim(x rarr 0)(sum(k =1)^(2016){(sinx)/x+2015k})/2016 is [...

    Text Solution

    |

  8. Lim(x rarr oo) (30+4sqrtx+7root(3)(x))/(2+sqrt(4x-7)+root(3)(6x-2) )eq...

    Text Solution

    |

  9. If Lim(x rarr0) ((a sin x + b tan x)/x^(3))= 3/2 then |a+2b| is equal ...

    Text Solution

    |

  10. lim(n rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is...

    Text Solution

    |

  11. Find the value of lim(n rarr oo)sum(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

    Text Solution

    |

  12. The value of Lim(x rarr 0)((tanx)^(1/x)+(1+sinx)^(x)) where x gt0 is e...

    Text Solution

    |

  13. If Lim(x rarr 0) (a sinx + bxe^(x)+3x^(2))/(sin x-2x+tanx) exists and ...

    Text Solution

    |

  14. If Lim(x rarr a) (sqrt(x-b)-sqrt(a-b))/(x^(2)-a^(2))(a gt b) = 1/64 an...

    Text Solution

    |

  15. If lim(x rarr 0) (k+cos lx)/x^(2)exists and has the value equal to -4 ...

    Text Solution

    |

  16. Lim(x rarr 0)((3sin x- sin 3x)^(4))/((sec x - cosx)^(6)) is equal to

    Text Solution

    |

  17. Lim(x rarr 0)(tanx sqrt (tanx)-sin x sqrt(sinx))/(x^(3).sqrtx) equals

    Text Solution

    |

  18. f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x)))." Then "underset(xtooo)l...

    Text Solution

    |