Infinite Limits — Question 6

Question 6 - Solution

We are asked to evaluate: $$\lim_{x \to -2^+} \frac{4}{(x + 2)^3}$$

Step 1: Analyze the denominator

As $x \to -2^+$, we approach $-2$ from the right, so: $$x + 2 \to 0^+ \quad \text{(a small positive number)}$$

Now consider the cube: $$(x + 2)^3 \to 0^+ \quad \text{(still positive, but very small)}$$

Step 2: Behavior of the expression

Since the numerator is positive and the denominator approaches a very small positive number: $$\frac{4}{(x + 2)^3} \to +\infty$$

Conclusion: $$\boxed{\lim_{x \to -2^+} \frac{4}{(x + 2)^3} = \infty}$$