Subjects calculus

Limit Evaluation B624Ba

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1. **State the problem:** Evaluate the limit $$\lim_{x \to -5} x(x - 5)(x + 3)$$. 2. **Recall the rule:** For polynomial functions, the limit as $x$ approaches a value is simply the value of the function at that point because polynomials are continuous everywhere. 3. **Substitute $x = -5$ directly into the expression:** $$(-5)((-5) - 5)((-5) + 3)$$ 4. **Simplify each factor:** $$(-5)(-10)(-2)$$ 5. **Multiply step-by-step:** $$(-5) \times (-10) = 50$$ 6. **Then multiply by the last factor:** $$50 \times (-2) = -100$$ 7. **Final answer:** $$\lim_{x \to -5} x(x - 5)(x + 3) = -100$$