From bf2d5f6c766fa446175acc4514af5e38c78efb04 Mon Sep 17 00:00:00 2001 From: Fang Liu Date: Fri, 29 Aug 2025 13:52:29 +0800 Subject: [PATCH] some typos --- quarto/limits/limits.qmd | 2 +- quarto/precalc/exp_log_functions.qmd | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/quarto/limits/limits.qmd b/quarto/limits/limits.qmd index 7b170e9..7e4bdb1 100644 --- a/quarto/limits/limits.qmd +++ b/quarto/limits/limits.qmd @@ -311,7 +311,7 @@ This progression can be seen to be increasing. Cauchy, in his treatise, can see $$ \begin{align*} -(1 + \frac{1}{m})^n &= 1 + \frac{1}{1} + \frac{1}{1\cdot 2}(1 - \frac{1}{m}) + \\ +(1 + \frac{1}{m})^m &= 1 + \frac{1}{1} + \frac{1}{1\cdot 2}(1 - \frac{1}{m}) + \\ & \frac{1}{1\cdot 2\cdot 3}(1 - \frac{1}{m})(1 - \frac{2}{m}) + \cdots \\ &+ \frac{1}{1 \cdot 2 \cdot \cdots \cdot m}(1 - \frac{1}{m}) \cdot \cdots \cdot (1 - \frac{m-1}{m}). diff --git a/quarto/precalc/exp_log_functions.qmd b/quarto/precalc/exp_log_functions.qmd index eb5750b..e3363a7 100644 --- a/quarto/precalc/exp_log_functions.qmd +++ b/quarto/precalc/exp_log_functions.qmd @@ -380,7 +380,7 @@ this by the inverse property. Whereas, by expressing $a=b^{\log_b(a)}$ we have: $$ -a^{(\log_b(x)/\log_b(b))} = (b^{\log_b(a)})^{(\log_b(x)/\log_b(a))} = +a^{(\log_b(x)/\log_b(a))} = (b^{\log_b(a)})^{(\log_b(x)/\log_b(a))} = b^{\log_b(a) \cdot \log_b(x)/\log_b(a) } = b^{\log_b(x)} = x. $$