#AP Calculus AB/BC: Selecting Procedures for Determining Limits 🚀

Hey there, future AP Calculus master! This guide is your ultimate resource for mastering limits, especially when you're down to the wire before the exam. Let's make sure you're not just ready, but confident.

#Unit 1: Limits - Your Foundation

This unit is the bedrock of calculus, and understanding limits is crucial. We'll recap the key methods for finding limits and then dive into how to choose the right one. Remember, you've got this! 💪

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#🔗 Unit 1 Overview: Limits & Continuity

If you need a quick refresher on the basics of limits, check out this link. But for now, let's focus on choosing the right method.

#Methods for Determining Limits

Here's a quick rundown of the techniques we've covered. Think of them as tools in your calculus toolkit. 🧰

#📈 1. Determining Limits From A Graph

It's all about what the function is *heading towards*, not necessarily the exact value at that point.

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#Visualizing Limits

Let's look at the graph of $y = \frac{1}{e^x}$:

Image Courtesy of Desmos

Example: As x approaches infinity, y approaches 0. Therefore, $\lim_{x \to \infty} \frac{1}{e^x} = 0$.

#📊 2. Estimating Limit Values From Tables

Look for patterns and the value y is approaching.

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#Analyzing Tables

Consider this table:

Image Courtesy of Coping With Calculus

Example: As x approaches 0, y approaches 2. So, we estimate that the limit is 2. ### 🧮 3. Determining Limits Using Algebraic Properties

Remember, limits play well with addition, subtraction, multiplication, and division. Also, don't forget composite functions!

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#Limit Laws:

• Sum: $\lim_{x \to c} [f(x) + g(x)] = \lim_{x \to c} f(x) + \lim_{x \to c} g(x)$
• Difference: $\lim_{x \to c} [f(x) - g(x)] = \lim_{x \to c} f(x) - \lim_{x \to c} g(x)$
• **Product:*...