Let's solve the three limit problems shown in the image.

1. Problem 1:

$\lim_{x \to -4} \frac{4 - |x|}{4 + x}$

Solution:

First, let's examine the expression:

• The term $|x|$ denotes the absolute value of $x$. Since $x \to -4$, we are approaching a negative value. Thus, $|x| = -x$ for $x < 0$.

Now, substitute $|x| = -x$ into the expression: $\lim_{x \to -4} \frac{4 - (-x)}{4 + x} = \lim_{x \to -4} \frac{4 + x}{4 + x}$

Simplify the fraction: $\lim_{x \to -4} 1 = 1$

So, the limit is 1.

2. Problem 2:

$\lim_{x \to 0} \left( \frac{2/x - 2}{|x|} \right)$

Solution:

Rewrite the expression inside the limit: $\frac{2/x - 2}{|x|} = \frac{2 - 2x}{x|x|}$

Let's consider the left-hand limit as $x \to 0$ from the negative side ($x \to 0^{-}$):

• Here, $|x| = -x$

Now the expression becomes: [ \frac{2/x - 2/|x|}=lim_{x->0} (x/|x|) Similarly for x to 0 then it becomes it converge to 0

3. Problem 3:

lim0 gives no clue to it.