Question

we now factor and cancel common factors.
lim_{x
ightarrow - 6^{+}}\frac{5x + 30}{x + 6}=lim_{x
ightarrow - 6^{+}}\frac{square(x + 6)}{x + 6}=lim_{x
ightarrow - 6^{+}}square=square

Explanation:

Step1: Factor the numerator

Factor out 5 from $5x + 30$ to get $5(x + 6)$. So, $\lim_{x
ightarrow - 6^{+}}\frac{5x + 30}{x + 6}=\lim_{x
ightarrow - 6^{+}}\frac{5(x + 6)}{x + 6}$.

Step2: Cancel common factors

Cancel out the common factor $(x + 6)$ in the numerator and denominator. We get $\lim_{x
ightarrow - 6^{+}}5$.

Step3: Evaluate the limit

Since the function $y = 5$ is a constant - function, for any value of $x$ approaching $-6$ from the right, the value of the function is 5. So, $\lim_{x
ightarrow - 6^{+}}5=5$.

Answer:

5