# Practice Demo

Find the following limit:
$$\lim_{x\to-3^+} \frac{3+x}{|3+x|}$$



Hint 1: For the function $\frac{3+x}{|3+x|}$, we are interested in what happens as $x$ approaches $-3$ from the right side.

Hint 2: The function $\frac{3+x}{|3+x|}$ has a discontinuity at $x=-3$.

Hint 3: Since the function is not continuous at $x=-3$, we cannot use the value of $f(x)$ at $x=-3$. Instead, we must find the value $\frac{3+x}{|3+x|}$ approaches as $x$ approaches $-3$ from the right side.

Solution:

The function $\frac{3+x}{|3+x|}$ approaches $1$ as $x$ approaches $-3$ from the right side.

Therefore:

$$\lim_{x\to-3^+} \frac{3+x}{|3+x|} = \color{blue}{1}$$