Let's take a very simple step-by-step explanation of the Limits lesson 👇 --- 🔹 What does Limit mean? The limit is the value that the function approaches when it gets close to a certain number. It means we don't have to reach the same point... the important thing is to "get closer to it". --- 🔹 A simple example If you have: f(x) = x^2 And we want to calculate: \lim_{x \to 2} x^2 We try values close to 2: f(x)=x2 1.9 3.61 1.99 3.9601 2.01 4.0401 👉 For every approximately 2, the result is approximately 4 ✔ Therefore: lim_{x \to 2} x^2 = 4 --- 🔹 Basic rule If the function is continuous, then: 👉 we put the value directly \lim_{x \to a} f(x) = f(a) --- 🔹 Example with a problem (0/0) \lim_{x \to 2} \frac{x^2 - 4}{x - 2} If we compensated: \frac{4 - 4}{2 - 2} = \frac{0}{0} ❌ This is called an indeterminate form. --- 🔹 How do we solve it? We analyze: x^2 - 4 = (x-2)(x+2) It remains: \frac{(x-2)(x+2)}{x-2} In short: = x + 2 Now let's calculate the final result: lim_{x \to 2} (x+2) = 4 --- 🔹 Types of endings 1. Normal ending 2. End from the right: \lim_{x \to a^+} \lim_{x \to a^-} 👉 Both must have the same value for the conclusion to exist. --- 🔹 Important example f(x) = \begin{cases} 1 & x < 0 \\ 2 & x > 0 \end{cases} 👉 From the north = 1 👉 From right to left = 2 ❌ The ending does not exist --- 🔹 Summary The limit = the value that the function approximates If there are no problems → compensate directly If it comes out 0/0 → Disassemble and analyze Right must equal left --- If you want: ✔ Solved exercises ✔ Or explain with a diagram ✔ Or a simple video