1. State the problem: Use the Constant Multiple Rule in limits, which states that $$\lim_{x \to a} [c \cdot f(x)] = c \cdot \lim_{x \to a} f(x)$$ where $c$ is a constant. 2. Example 1: $$\lim_{x \to 2} 3x = 3 \cdot \lim_{x \to 2} x = 3 \cdot 2 = 6$$ 3. Example 2: $$\lim_{x \to 0} 5\sin x = 5 \cdot \lim_{x \to 0} \sin x = 5 \cdot 0 = 0$$ 4. Example 3: $$\lim_{x \to 1} -4x^2 = -4 \cdot \lim_{x \to 1} x^2 = -4 \cdot 1 = -4$$ 5. Example 4: $$\lim_{x \to 3} 7\sqrt{x} = 7 \cdot \lim_{x \to 3} \sqrt{x} = 7 \cdot \sqrt{3}$$ 6. Example 5: $$\lim_{x \to -1} 2e^x = 2 \cdot \lim_{x \to -1} e^x = 2 \cdot e^{-1} = \frac{2}{e}$$ 7. Example 6: $$\lim_{x \to 4} -6\frac{1}{x} = -6 \cdot \lim_{x \to 4} \frac{1}{x} = -6 \cdot \frac{1}{4} = -\frac{3}{2}$$ 8. Example 7: $$\lim_{x \to 0} 8\cos x = 8 \cdot \lim_{x \to 0} \cos x = 8 \cdot 1 = 8$$ 9. Example 8: $$\lim_{x \to 5} 10\ln x = 10 \cdot \lim_{x \to 5} \ln x = 10 \cdot \ln 5$$ 10. Example 9: $$\lim_{x \to 2} -9x^3 = -9 \cdot \lim_{x \to 2} x^3 = -9 \cdot 8 = -72$$ 11. Example 10: $$\lim_{x \to 1} 4\tan x = 4 \cdot \lim_{x \to 1} \tan x = 4 \cdot \tan 1$$ Answer: The Constant Multiple Rule allows us to take the constant outside the limit and multiply it by the limit of the function. This simplifies limit calculations when a constant multiplier is present.