1. The problem is to understand and apply the theorem on limits: $$\lim_{x \to a} c = c$$ where $c$ is a constant and $a$ is the point $x$ approaches. 2. This theorem states that the limit of a constant function as $x$ approaches any value $a$ is simply the constant itself. 3. Important rule: Since the function does not depend on $x$, the value does not change as $x$ approaches $a$. 4. To practice, evaluate limits of constant functions at various points: Examples: 1. $$\lim_{x \to 2} 5 = 5$$ 2. $$\lim_{x \to -3} 7 = 7$$ 3. $$\lim_{x \to 0} -4 = -4$$ 4. $$\lim_{x \to 10} 0 = 0$$ 5. $$\lim_{x \to 1} 12 = 12$$ 6. $$\lim_{x \to -1} 3.14 = 3.14$$ 7. $$\lim_{x \to 100} -9 = -9$$ 8. $$\lim_{x \to 0.5} 8 = 8$$ 9. $$\lim_{x \to -5} 1 = 1$$ 10. $$\lim_{x \to 7} -2 = -2$$ 11. $$\lim_{x \to 3} 6 = 6$$ 12. $$\lim_{x \to -10} 15 = 15$$ 13. $$\lim_{x \to 4} -7 = -7$$ 14. $$\lim_{x \to 0} 9 = 9$$ 15. $$\lim_{x \to 8} 11 = 11$$ 16. $$\lim_{x \to -2} 0.5 = 0.5$$ 17. $$\lim_{x \to 6} -3 = -3$$ 18. $$\lim_{x \to 9} 4 = 4$$ 19. $$\lim_{x \to 5} -1 = -1$$ 20. $$\lim_{x \to -7} 2 = 2$$ 5. Each example shows the limit of a constant function at a point, reinforcing the theorem. Final answer: For any constant $c$ and any point $a$, $$\lim_{x \to a} c = c$$.