1. The problem is to understand what special limits are in calculus. 2. Special limits are particular limits that frequently appear and have well-known results, which help in solving more complex limit problems. 3. Two common special limits are: - $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$ - $$\lim_{x \to 0} (1 + x)^{\frac{1}{x}} = e$$ 4. These limits are important because they form the basis for defining derivatives of trigonometric and exponential functions. 5. For example, the first limit shows that near zero, $$\sin x$$ behaves like $$x$$, which is crucial for differentiating sine. 6. The second limit defines the number $$e$$, the base of natural logarithms, which is fundamental in calculus and exponential growth. 7. Understanding these special limits allows you to evaluate more complicated limits by rewriting expressions to use these forms. Final answer: The special limits are $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$ and $$\lim_{x \to 0} (1 + x)^{\frac{1}{x}} = e$$.