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Math Help - Simple limit problem

  1. #1
    Junior Member Greg98's Avatar
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    Simple limit problem

    Hello, this basic limit problem puzzles me:

    <br />
\lim_{x\rightarrow \ -2} \frac{x-1}{x+2}<br />

    My intuition says, that there isn't limit on this spot, because I couldn't modify(tried factorize or divide with x etc.) expression to shape, where the function is defined. Graphing the function didn't help either. But, maybe there is some way...? Any help is appreciated, thanks!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Greg98 View Post
    Hello, this basic limit problem puzzles me:

    <br />
\lim_{x\rightarrow \ -2} \frac{x-1}{x+2}<br />

    My intuition says, that there isn't limit on this spot, because I couldn't modify(tried factorize or divide with x etc.) expression to shape, where the function is defined. Graphing the function didn't help either. But, maybe there is some way...? Any help is appreciated, thanks!
    As x approaches -2 the denominator is getting closer to zero while the numerator is getting (slightly) more negative.

    And we know what happens when we divide by an increasingly small denominator
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