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Math Help - Limits using absolute values

  1. #1
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    Limits using absolute values

    find limit if limit exists:

    limit[x:-[infinity]](|x-2|+|3x|)/(x)
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  2. #2
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    I assume that this is the question: \lim _{x \to  - \infty } \frac{{\left| {x - 2} \right| + \left| {3x} \right|}}{x}.
    Note that x < 0 \Rightarrow \quad x =  - \left| x \right|. Which gives: \frac{{\left| {x - 2} \right| + \left| {3x} \right|}}<br />
{x} =  - \left[ {\frac{{\left| {x - 2} \right| + \left| {3x} \right|}}<br />
{{\left| x \right|}}} \right] =  - \left[ {\left| {1 - \frac{2}<br />
{x}} \right| + \left| 3 \right|} \right].
    Now you finish.
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