Home
Class 12
MATHS
The value of lim(xrarr3) ((x^(3)+27)log(...

The value of `lim_(xrarr3) ((x^(3)+27)log_(e)(x-2))/(x^(2)-9)` is

A

9

B

18

C

27

D

`5//3`

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xrarr3)(lim)((x^(3)+27)log_(e)(x-2))/((x^(2)-9))`
`=underset(xrarr3)(lim)((x+3)(x^(2)+9-3x)log_(e)(1+(x-3)))/((x+3)(x-3))`
`=underset(xrarr3)(lim)(x^(2)+9-6x)`
`=18-9=9`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|24 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise ComprehensionType|2 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED|2 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(x->3)((x^3+27)(log)_e(x-2))/(x^2-9) is a. 9 b. 18 c. 27 d. 1/3

Value of lim_(xrarr2)[x] is

The value of lim_(xrarr0)(1-cos(x/3))/x^2'

The value of lim_(xrarr3)(sqrt(x+3)+sqrt(x-3))/x is

Value of lim_(x rarr 3)(sin(e^(x-3) -1))/log(x-2) is

The value of lim_(xto4) (x^(7//2)-4 ^(7//2))/(log _(e) (x-3)) is-

The value of lim_(xrarr0)(sin5x)/(tan 3x) is

The value of lim_(x to oo ) (x-x^(2)log_(e)(1+(1)/(x))) is _______.

The value of lim_(xrarr0)(1-cos4x)/x^2 is

The value of lim_(xrarr0)(1-cos4x)/x^2 is

CENGAGE PUBLICATION-LIMITS-Single Correct Answer Type
  1. If a(n) and b(n) are positive integers and a(n)+sqrt2b(n)=(2+sqrt2)^(n...

    Text Solution

    |

  2. The value of lim(x rarr 0) ((tanx^((1)/(5)))/((tan^(-1)sqrtx)^(2))(log...

    Text Solution

    |

  3. The value of lim(xrarr3) ((x^(3)+27)log(e)(x-2))/(x^(2)-9) is

    Text Solution

    |

  4. The value of lim(xrarr0^(+))((1-cos(sin^(2)x))/(x^(2)))^((log(e)(1-2x^...

    Text Solution

    |

  5. underset(xrarr0)(lim)(1)/(x^(2))|(1-cos3x,log(e)(1+4x)),(sin^(-1)(e^(x...

    Text Solution

    |

  6. If graph of the function y=f(x) is continuous and passes through point...

    Text Solution

    |

  7. Let f(x) be defined for all x in R such that lim(xrarr0) [f(x)+log(1-(...

    Text Solution

    |

  8. lim(xrarroo) x^(2)sin(log(e)sqrt(cos(pi)/(x)))

    Text Solution

    |

  9. If lim(xrarroo) ((x+c)/(x-c))^(x)=4 then the value of e^(c) is

    Text Solution

    |

  10. If lim(xrarr0) [1+x+(f(x))/(x)]^(1//x)=e^(3)", then "lim(xrarr0) [1+(f...

    Text Solution

    |

  11. lim(xrarr(pi)/(2)) [1+(cosx)^(cosx)]^(2)=

    Text Solution

    |

  12. If agt0, b gt0 than lim(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

    Text Solution

    |

  13. If f(x)=lim(nrarroo) (cos(x)/(sqrtn))^(n), then the value of lim(xrarr...

    Text Solution

    |

  14. lim(xrarr0) (log(e^(x^(2))+2sqrtx))/(tansqrtx) is equal to

    Text Solution

    |

  15. Let f:RrarrR be such that f(a)=1, f(a)=2. Then lim(x to 0)((f^(2)(a+x)...

    Text Solution

    |

  16. L=underset(nrarroo)(lim)((sqrt(n^(2)+n)-1)/(n))^(2sqrt(n^(2)+n)-1)

    Text Solution

    |

  17. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

    Text Solution

    |

  18. lim(nrarroo) (1-x+x.root n e)^(n) is equal to

    Text Solution

    |

  19. The value of lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

    Text Solution

    |

  20. The value of underset(xrarr1)(lim)(root(2)x-root4x)/(root3x-root2x) is

    Text Solution

    |