Home
Class 12
MATHS
Evaluate lim(x to 3) (x^(3) - 7x^(2) + ...

Evaluate `lim_(x to 3) (x^(3) - 7x^(2) + 15x - 9)/(x^(4) - 5x^(3) + 27 x - 27)`

Text Solution

Verified by Experts

The correct Answer is:
`(2)/(9)`

`underset(x to 3)(lim) ((x - 3)^(2)(x - 1))/((x - 3)^(3)(x^(2) + x - 3))`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise SECTION - A|50 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - B|34 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Example|41 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos

Similar Questions

Explore conceptually related problems

lim_(x to 3) (x^(3) - x^(2) + 15 x - 9)/(x^(4) - 5x^(3) + 27x - 27) is equal to

Evaluate lim_(xto-3) (x^(3)+27)/(x^(5)+243)

Evaluate lim_(x to 2) [4x^(2) + 3x + 9]

lim_(x rarr3)(x^(3)-7x^(2)+15x-9)/(x^(4)-5x^(3)+27x-27) is equal to:

Evaluate lim_(x to 0) [(3x^(2) + 4x + 5)/(x^(2) - 2x + 3)]

Evaluate lim_(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) 9x^(4) - x^(3) + 35x^(2) + 6x + 30)/(x^(5) - 2x^(4) + 4x^(2) - 9x + 6)

Evaluate: lim_(x rarr 3) [(x^(3)-27)/(x-3)] .

lim_(x rarr3)(x^(3)-27)/(x^(2)-9)

lim_(x to 3) (x^(2) - 27)/(x^(2) - 9) is equal to

Evaluate: lim_(xrarr3) (x^(2)-4x+3)/(x^(2)+6x- 27)

AAKASH INSTITUTE-LIMITS AND DERIVATIVES -Try yourself
  1. Evaluate lim(x to 2) (x^(2) - 4) [(1)/(x + 2) + (1)/(x - 2)]

    Text Solution

    |

  2. Evaluate lim(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) 9x^(4) ...

    Text Solution

    |

  3. Evaluate lim(x to 3) (x^(3) - 7x^(2) + 15x - 9)/(x^(4) - 5x^(3) + 27 ...

    Text Solution

    |

  4. Evaluate lim(x to 4) (x^(5) - 1024)/(x - 5)

    Text Solution

    |

  5. Evaluate lim(x to 16) (x^(3//2) - 64)/(x - 16)

    Text Solution

    |

  6. Evaluate lim(x to 0) (1 - x^(n) - 1)/(x)

    Text Solution

    |

  7. Evaluate lim(x to a) ((x + 4)^(5//4) - (a + 4)^(5//4))/(x - a)

    Text Solution

    |

  8. If lim(x to 3) (X^(n) - 3^(n))/(x - 3) = 405 and n in N Find n

    Text Solution

    |

  9. If lim(x to 2) (X^(n) - 2^(n))/(x - 2) = 448 and n in N , find n

    Text Solution

    |

  10. If lim(x to a) (x^(5) + a^(5))/(x + a) = 405, Find the value of a.

    Text Solution

    |

  11. If lim(x to 0) (x^(9) + a^(9))/(x + a) = 9, find the value of a

    Text Solution

    |

  12. If lim(x to 2) (x - 2)/(""^(3)sqrt(x) - ""^(3)sqrt(2)) = lim(x to k) ...

    Text Solution

    |

  13. If lim(x to a) (xsqrt(x) - a sqrt(a))/(x - 1) = lim(x to 3) (x^(3) -...

    Text Solution

    |

  14. Evaluate lim(x to 2) (sqrt(3 - x) - 1)/(2 - x)

    Text Solution

    |

  15. Evaluate lim(x to 3) (sqrt(x + 3) - sqrt(6))/(x^(2) - 9)

    Text Solution

    |

  16. Evaluate lim(x to 0) (tan 5x)/(2x)

    Text Solution

    |

  17. Evaluate lim(x to 0) ("sin"ax)/(x)

    Text Solution

    |

  18. Evaluate lim(x to 0) ("sin"^(2) 4x)/(x^(2))

    Text Solution

    |

  19. Evaluate lim(x to 0) ("sin"(5x)/(4))/(x^(2))

    Text Solution

    |

  20. Evaluate lim(x to 0) ("sin"^(2) ax)/("sin"^(2) bx)

    Text Solution

    |