Evaluate the following limits: 5. x 0^+ |x|, x 0^- |x| 6. x 2^+ |x - 2|, x 2^- |x - 2| 7. _x 0^+ (|x|)/(x)

$$
\lim_{x \to 0^+} |x| = \lim_{x \to 0^+} x
$$

$$
\lim_{x \to 0^+} x = 0
$$
The limit is $\boxed{\text{0}}$.

$$
\lim_{x \to 0^-} |x| = \lim_{x \to 0^-} (-x)
$$

$$
\lim_{x \to 0^-} (-x) = -(0) = 0
$$
The limit is $\boxed{\text{0}}$.

$$
\lim_{x \to 2^+} |x - 2| = \lim_{x \to 2^+} (x - 2)
$$

$$
\lim_{x \to 2^+} (x - 2) = 2 - 2 = 0
$$
The limit is $\boxed{\text{0}}$.

$$
\lim_{x \to 2^-} |x - 2| = \lim_{x \to 2^-} -(x - 2)
$$

$$
\lim_{x \to 2^-} -(x - 2) = -(2 - 2) = -(0) = 0
$$
The limit is $\boxed{\text{0}}$.

$$
\lim_{x \to 0^+} \frac{|x|}{x} = \lim_{x \to 0^+} \frac{x}{x}
$$

$$
\lim_{x \to 0^+} \frac{x}{x} = \lim_{x \to 0^+} 1
$$

$$
\lim_{x \to 0^+} 1 = 1
$$
The limit is $\boxed{\text{1}}$.

$$
\lim_{x \to 0^-} \frac{|x|}{x} = \lim_{x \to 0^-} \frac{-x}{x}
$$

$$
\lim_{x \to 0^-} \frac{-x}{x} = \lim_{x \to 0^-} (-1)
$$

$$
\lim_{x \to 0^-} (-1) = -1
$$
The limit is $\boxed{\text{-1}}$.