Multivariable Limits: The Two-Path Trap (and the 4-Step Method That Always Works)

Описание: Let’s tackle multivariable limits together, step by step. I’ll show you why testing the x-axis and y-axis is almost never enough (the “Two-Path Trap”), and why matching limits along ten different lines still proves absolutely nothing.

Instead of guessing, we’ll build a reliable 4-step decision tree that tells you exactly what to do. You’ll learn when you can simply plug the numbers in, how to use the family of lines (y=mx) to disprove a limit instantly, when to switch to curved paths, and how to rigorously prove a limit exists using algebra or the Squeeze Theorem with polar coordinates.

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For full lessons, quizzes, and step-by-step practice:
Calculus 3 (Multivariable Calculus) → https://courses.kristakingmath.com/li...

WHAT YOU'LL LEARN
The 4-step decision tree for solving any multivariable limit
Why matching paths (like the axes) does not prove a limit exists
How to use the family of lines (y=mx) to disprove a limit quickly
The “Power-Match” tool for choosing curved paths
How to use algebraic simplification to show the limit exists (even at a discontinuity)
How to use the Polar Decision Rule to prove existence (or non-existence)

CHAPTERS
0:46 — Step 1: Direct Substitution
1:40 — Step 2: Disproving with Paths: Testing the Axes
3:29 — Step 2: Disproving with Paths: Testing All Lines
5:58 — Step 2: Disproving with Paths: Testing Curves
7:53 — Step 3: How to Prove a Limit Exists (Algebra)
10:07 — Step 4: The Ultimate Proof (Polar Coordinates)
13:59 — Step 4: Polar Case 2 (The Limit Does Not Exist)
16:04 — (Challenge) Proving with Squeeze Theorem (Using a Famous Inequality)
23:06 — Your 4-Step Toolkit (Recap)

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