Easiest Way to Understand Limits and Derivatives
1. Limits (Approaching a Value)
Think of limits as "getting closer to a value" without necessarily reaching it.
Example: $\lim\limits_{x \rightarrow 2}\left(x^2\right)=4$, as $x^2$ gets closer to 4 when $x$ approaches 2 .
Use substitution first; if it gives $\frac{0}{0}$, try factoring or rationalizing.
2. Derivatives (Rate of Change)
The derivative measures how a function changes at a point (slope of a curve).
Formula: $f^{\prime}(x)=\lim\limits_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$.
Start with simple functions like $x^2$ to see patterns in differentiation.