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Math Help - Limit question

  1. #1
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    Limit question

    As limit x approaches -3 from the left hand side (x+2)/(x+3), The limit is positive infinity.
    And if it approaches -3 from the right hand side its negative infinity.
    Why is that ? Could someone please explain it to me?
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  2. #2
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    Simple. Since you approach from the left of -3, try to think of a number right next to -3, like -3.1
    Then, you see that If you solve for that number, your value in the denominator will be a very small negative number.
    Then, in the numerator the number will be a negative number.
    So, since you divide a number by a very small number that is extremely close to zero, you get infinity, and since both are negative, they cancel and you get possitive infinity.
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  3. #3
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    Why not take a look at the graph of the function? The reasoning will be obvious...
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    Quote Originally Posted by letzdiscuss View Post
    As limit x approaches -3 from the left hand side (x+2)/(x+3), The limit is positive infinity.
    And if it approaches -3 from the right hand side its negative infinity.
    Why is that ? Could someone please explain it to me?
    y = \frac{x+2}{x+3} = 1 - \frac{1}{x+3} is a hyperbola and it's graph will give the answer to your question.
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