Limits using absolute values

**Roxanne** · Sep 22nd 2008, 07:16 AM

find limit if limit exists:

limit[x:-[infinity]](|x-2|+|3x|)/(x)

**Plato** · Sep 22nd 2008, 07:33 AM

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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