Question 2 Evaluate the following limits: \( 2.1 \lim _{x \rightarrow 3}\left(x^{3}+2\right)\left(x^{2}-5 x\right) \). \( 2.2 \lim _{x \rightarrow-4^{-}}\left(\frac{|x+4|}{x+4}\right) \.

We are given two limits to evaluate. 2.1: Evaluate limₓ → 3 [(x³ + 2)(x² - 5x)]. Step 1: Factor and substitute x = 3. • Compute x³ + 2 when x = 3: 3³ + 2 = 27 + 2 = 29. • Compute x² - 5x when x = 3: 3² - 5(3) = 9 - 15 = -6. Step 2: Multiply the results: 29 × (-6) = -174. Therefore, limₓ → 3 [(x³ + 2)(x² - 5x)] = -174. 2.2: Evaluate limₓ → -4⁻ (|x + 4|/(x + 4)). Step 1: Understand the behavior as x approaches -4 from the left. Since x → -4⁻, it means x is slightly less than -4, so (x + 4) is negative (but not zero). Step 2: Use the definition of absolute value. For any negative number u, |u| = -u. Let u = x + 4 which is negative, then |x + 4| = -(x + 4). Step 3: Rewrite the fraction:   |x + 4|/(x + 4) = [-(x + 4)]/(x + 4) = -1. Thus, the limit evaluates to -1. Final Answers: 2.1: -174 2.2: -1