1. The problem is to explain what simple approximations are and how to perform them. 2. Simple approximations involve replacing complicated expressions with simpler ones that are close enough to the original for practical purposes. 3. For example, for very small $x$, we approximate $\sin x \approx x$ because their values are very close when $x$ is near zero. 4. Another example is using $\sqrt{1 + x} \approx 1 + \frac{x}{2}$ for small $x$, which comes from the binomial expansion. 5. These approximations help simplify calculations and understand relationships without complex computations.