#AP Calculus AB/BC: Mastering Limits Algebraically 🚀

Hey there, future AP Calculus master! Let's dive into the world of limits, but this time, we're ditching the graphs and going full algebra mode. This guide is your go-to resource for acing those limit problems on the AP exam. Let's get started!

#1.5 Algebraic Properties of Limits

# 🔍 Finding Limits with Algebra

The core idea? Plug in the value that x is approaching. It's that simple! But, to make it super smooth, we have a set of rules that help us break down complex limits into simpler parts. Think of these rules as your algebraic superpowers.

#Limit Laws: Your Algebraic Toolkit

If $lim_{x \to c} f(x) = L$ and $lim_{x \to c} g(x) = M$, where L, M, and c are real numbers, then:

• Sum Rule: $lim_{x \to c} [f(x) + g(x)] = L + M$
• Difference Rule: $lim_{x \to c} [f(x) - g(x)] = L - M$
• Constant Multiple Rule: $lim_{x \to c} [k \cdot f(x)] = k \cdot L$
• Product Rule: $lim_{x \to c} [f(x) \cdot g(x)] = L \cdot M$
• Quotient Rule: $lim_{x \to c} \frac{f(x)}{g(x)} = \frac{L}{M}$, provided $M \neq 0$
• Power Rule: $lim_{x \to c} [f(x)]^n = L^n$, where n is a positive integer
• Root Rule: $lim_{x \to c} \sqrt[n]{f(x)} = \sqrt[n]{L} = L^{\frac{1}{n}}$