Home
Class 12
MATHS
lim(xtooo) (x(logx)^(3))/(1+x+x^(2)) equ...

`lim_(xtooo) (x(logx)^(3))/(1+x+x^(2))` equals

A

`underset(xto0^(+))f(x)=1`

B

`underset(xto0^(-))limf(x)=cot1`

C

`cot^(-1)(underset(xto0^(-))f(X))^(2)=1`

D

`tan^(-1)(underset(xto0^(+))f(x))=(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xtooo)lim((log)^(3)+x.3(logx)^(2)xx(1)/(x))/(1+2x)" "`(Using L'Hospital's rule)
`=underset(xtooo)lim(3(logx)^(2)xx(1)/(x)+6(logx)xx(1)/(x))/(2)`
`=underset(xtooo)lim(3(log)^(2)+6logx)/(2x)`
`=underset(xtooo)lim(6logxxx(1)/(x)+(6)/(x))/(2)" "`(Using L'Hospital's rule)
`=underset(xtooo)lim(6logx+6)/(2x)`
`=underset(xtooo)lim(6((1)/(x))+0)/(2)" "`(Using L'Hospital's rule)
`=((6)/(oo))/(2)=0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|24 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|20 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.8|8 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

lim_(x to 0) (log (1 + 2x))/(x) + lim_(x to 0) (x^(4) - 2^(4))/(x - 2) equals

The value of lim_(x to 0) ((1)/(x^(2)) - cot x) equals

lim_(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

Evaluate lim_(xtooo) (log_(e)x)/(x)

The value of lim_(x to 1) (x^(5) - 3x + 2)/(x - 1) equals

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

Let f(x) be a polynomial satisfying lim_(xtooo) (x^(2)f(x))/(2x^(5)+3)=6" and "f(1)=3,f(3)=7" and "f(5)=11. Then The value of f(0) is

lim_(x to 2) (x^(2) - 4)/(x + 3) is equal to

lim_(x to 1//2) (8x^(3) - 1)/(16 x^(4) - 1) is equal to

CENGAGE ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

    Text Solution

    |

  2. The value of lim(ntooo) [(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^...

    Text Solution

    |

  3. lim(xto1) (nx^(n-1)-(n+1)x^(n)+1)/((e^(x)-e)sinpix), where n=100,is eq...

    Text Solution

    |

  4. lim(xto0) (log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)=

    Text Solution

    |

  5. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

    Text Solution

    |

  6. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

    Text Solution

    |

  7. If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo then lim(xtoa){f(x)}^(g(x))=e^...

    Text Solution

    |

  8. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

    Text Solution

    |

  9. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

    Text Solution

    |

  10. lim(xto0) ((1+tanx)/(1+sinx))^(cosecx) is equal to

    Text Solution

    |

  11. The value of lim(xto1) (2-x)^(tan((pix)/(2))) is

    Text Solution

    |

  12. The value of lim(mtooo) ("cos"(x)/(m))^(m) is

    Text Solution

    |

  13. lim(ntooo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is equal to

    Text Solution

    |

  14. lim(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ) is ...

    Text Solution

    |

  15. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is

    Text Solution

    |

  16. lim(x->0)((1^x+2^x+3^x+....+n^x)/n)^(1/x)

    Text Solution

    |

  17. The value of lim(x to 1) ((p)/(1-x^(p))-(q)/(1-xq)),p,q,inN, equals

    Text Solution

    |

  18. lim(xtooo) (x(logx)^(3))/(1+x+x^(2)) equals

    Text Solution

    |

  19. lim(x->oo)cot^(-1)(x^(-a)loga x)/(sec^(-1)(a^xlogx a)),(a >1)is equal ...

    Text Solution

    |

  20. The value of lim(ntooo)(e^(n))/((1+(1)/(n))^(n^(2)))is (a) -1 (b) 0 ...

    Text Solution

    |