Mathematics has so many theorems, properties, and formulas to memorize. When solving math problems, you need to apply the theorems, properties, and formulas you have learned. When studying new concepts, proofs, or derivations in a textbook, you also rely on the theorems and properties you have learned. If you forget these theorems and properties, you might not be able to understand the derivations of formulas. However, sometimes your memory becomes fuzzy, and you can't recall the conditions of a property or the correct application of a formula. You urgently need to find the source of this formula or theorem quickly. But at that moment, you can't remember which book the theorem is from, or which chapter of the textbook it’s in. You might think it’s in Chapter 3, but you can’t find the theorem anywhere in that chapter! What should you do in such a situation? Sometimes, I spend a lot of time just trying to find the source of a particular property!
For example, you come across a math problem that could be solved quickly by applying a certain property. However, your memory is unclear—you’re not sure if such an equation actually exists. Or perhaps you can’t remember the prerequisites for using this equation, such as the conditions on g(x) or any restrictions on f(x). At this point, you need to locate the source of this property in a math book to verify it. You might suggest looking under topics like "Limits of Composite Functions" or "Composite Functions." Of course, that could work if you’re lucky enough to remember a few keywords. But you can’t always rely on luck. Some formulas, theorems, and properties are listed in textbooks as "Theorem 1" or "Property 3," without memorable keywords. In such cases, the effort required to find their source becomes much greater!$$\lim_{x\to c}f\big(g(x)\big)=f\big(\lim_{x\to c}g(x)\big)$$