Home
Class 11
MATHS
Evaluate the following limit: underset( ...

Evaluate the following limit: `underset( x rarr a) ( "lim")((x+2)^(5//2)-(a+2)^(5//2))/(x-a)`

Text Solution

Verified by Experts

Given limit: `lim_(x->a)((x+2)^(5/2)-(a+2)^(5/2))/(x-a)`
Substituting `a` as we get an indeterminant form of `(0/0)`
As it has come as `(0/0)` form ,so we use L’Hospitals Rule.
now by using L’Hospitals Rule the limit is given by,
`l=lim_(x->a)(5/2)(x+2)^(3/2)`
`=(5/2)(a+2)^(3/2)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limit: (lim)_(x rarr2)(3-x)

Evaluate the following limit: (lim)_(x rarr a)((x+2)^(3)-(a+2)^(3/2))/(x-a)

Evaluate the following limits : lim_(x rarr 1) [1/(x-1)-2/(x^2-1)]

Evaluate the following limits: lim_(x rarr((pi)/(2)))tan x

Evaluate the following limits: lim_(xrarra){((x+2)^(5//3)-(a+2)^(5//3))/(x-a)}

Evaluate the following limits: lim_(xrarra)((x^(5//2)-a^(5//2))/(x-a))

Evaluate the following limits : lim_(x rarr 2) (x^2-x-2)/ (x^2-3x+2)

Evaluate the following limit: (lim)_(x rarr0)(a^(x)+b^(x)-2)/(x^(2))

Evaluate the following limit: (lim)_(x rarr0)((a+x)^(2)-a^(2))/(x)

Evaluate the following limit: (lim)_(x rarr0)(sin^(2)4x^(2))/(x^(4))

RD SHARMA-LIMITS-All Questions
  1. Evaluate:underset( x rarr 2) ( "lim") (x-2)/(root(3)(x)-root(3)(33))

    Text Solution

    |

  2. If underset( x rarr - a) ( "lim")(x^9+a^9)/(x+a)=9,\ find the real va...

    Text Solution

    |

  3. Evaluate the following limit: underset( x rarr a) ( "lim")((x+2)^(5//2...

    Text Solution

    |

  4. Evaluate the following limit: underset( x rarr 0)((1+x)^6-1)/((1+x)^2-...

    Text Solution

    |

  5. Evaluate the following limit: (lim)(x->a)(x^(5//7)-a^(5//7))/(x^(2//7)...

    Text Solution

    |

  6. Evaluate (i) lim(x""->1)(x^(15)-1)/(x^(10)-1) (ii) lim(x""->0)(sqrt(...

    Text Solution

    |

  7. Evaluate the following limit: (lim)(x->a)(x^(2//3)-a^(2//3))/(x^(3//4)...

    Text Solution

    |

  8. Evaluate the following limit: lim(x->a)((x+2)^(3//2)-(a+2)^(3//2))/(x-...

    Text Solution

    |

  9. Evaluate the following limit: lim(x->a)(x^(2//7)-a^(2//7))/(x-a)

    Text Solution

    |

  10. Evaluate the following limit: lim(x->-1//2)(8x^3+1)/(2x+1)

    Text Solution

    |

  11. Evaluate the following limit: lim(x->-1//2)(8x^3+1)/(2x+1)

    Text Solution

    |

  12. Evaluate the following limit: lim(x->4)(x^3-64)/(x^2-16)

    Text Solution

    |

  13. Evaluate the following limit: lim(x->-1)(x^3+1)/(x+1)

    Text Solution

    |

  14. If lim(x->a) (x^5-a^5)/(x-a)=5, then find the sum of theIf lim-possi...

    Text Solution

    |

  15. If lim(x->a) (x^5-a^5)/(x-a)=5, then find the sum of theIf lim-possi...

    Text Solution

    |

  16. If lim(x->a)(x^9-a^9)/(x-a)=\ lim(x->5)(4+x) find all possible values ...

    Text Solution

    |

  17. If lim(x->a)(x^3-a^3)/(x-a)=lim(x->1)(x^4-1)/(x-1) , find all possible...

    Text Solution

    |

  18. Evaluate : lim(x->oo)(a x^2+b x+c)/(dx^2+e x+f)dot

    Text Solution

    |

  19. Evaluate the following limit: lim(x->oo)((3x-1)(4x-2))/((x+8)(x-1))

    Text Solution

    |

  20. Evaluate the following limit: lim(x->oo)(5x^3-6)/(9+4x^3 )\

    Text Solution

    |