From b905897a3a320843c12952245103c0dd9d4b2f77 Mon Sep 17 00:00:00 2001 From: Hugh Ratsch Date: Sun, 23 Mar 2025 20:22:41 -0500 Subject: [PATCH] Fix equation formatting for better Gitea rendering --- calculus_lesson_1.md | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/calculus_lesson_1.md b/calculus_lesson_1.md index 4d11f6b..af6089c 100644 --- a/calculus_lesson_1.md +++ b/calculus_lesson_1.md @@ -48,12 +48,10 @@ $\lim_{x \to a} f(x) = L$ if and only if $\lim_{x \to a^-} f(x) = \lim_{x \to a^ ## Example: A Piecewise Function -Consider: -$$g(x) = -\begin{cases} -x^2, & \text{if } x < 1 \\ -3x-1, & \text{if } x \geq 1 -\end{cases}$$ +Consider the function g(x) defined as: + +$$g(x) = x^2 \text{ for } x < 1$$ +$$g(x) = 3x-1 \text{ for } x \geq 1$$ Let's find $\lim_{x \to 1} g(x)$: @@ -67,7 +65,7 @@ Since the left and right limits are different (1 ≠ 2), $\lim_{x \to 1} g(x)$ d Limits don't exist when: 1. Left and right limits are different (as in our example above) 2. The function oscillates infinitely at the point (like $\sin(1/x)$ as x approaches 0) -3. The function grows without bound (like $1/x^2$ as x approaches 0) +3. The function grows without bound (like $\frac{1}{x^2}$ as x approaches 0) ## Basic Limit Laws