Key Concepts of Limits in Year 9 Calculus

1. What are Limits?
   A limit shows what value a function gets close to when the input gets near a certain number.

2. How to Write Limits:
   Limits are written like this: $\lim_{x \to a} f(x) = L$.
   This means that as $x$ gets closer to $a$, the function $f(x)$ gets closer to $L$.

3. Different Types of Limits:

   • One-Sided Limits:
     You can look at limits from one side.
     For example, $\lim_{x \to a^-} f(x)$ looks at what happens when you come from the left.
     And $\lim_{x \to a^+} f(x)$ looks at what happens when you come from the right.
   • Infinite Limits:
     These limits describe what happens when $f(x)$ gets really big, or close to infinity.

4. What is Continuity?
   A function is continuous at a point $a$ if $\lim_{x \to a} f(x) = f(a)$.
   This means that there are no breaks or jumps in the graph at that point.

5. Why Limits Matter:
   Knowing about limits is important in areas like physics and engineering.
   They help us understand how things change and behave at certain points.