Final Answer:
1. $\lim_{x \to 3^+} \frac{-5}{x+3} = -\frac{5}{6}$, $\lim_{x \to 3^-} \frac{-5}{x+3} = -\frac{5}{6}$, $\lim_{x \to 3} \frac{-5}{x+3} = -\frac{5}{6}$
2. $\lim_{x \to 5^+} \frac{4}{(5-x)^3} = -\infty$, $\lim_{x \to 5^-} \frac{4}{(5-x)^3} = +\infty$, $\lim_{x \to 5} \frac{4}{(5-x)^3}$ does not exist
3. $\lim_{x \to 2^+} \frac{3x}{x-2} = +\infty$, $\lim_{x \to 2^-} \frac{3x}{x-2} = -\infty$, $\lim_{x \to 2} \frac{3x}{x-2}$ does not exist
4. $\lim_{x \to 4^+} \frac{8}{(x-4)^7} = +\infty$, $\lim_{x \to 4^-} \frac{8}{(x-4)^7} = -\infty$, $\lim_{x \to 4} \frac{8}{(x-4)^7}$ does not exist
Parent Tip: Review the logic above to help your child master the concept of limits at infinity worksheet.