edits, add dark mode

quarto/derivatives/newtons_method.qmd

@@ -864,7 +864,7 @@ The calculation that produces the quadratic convergence now becomes:
 
 $$
 \begin{align*}
-x_{i+1} - \alpha &= (x_i - \alpha) - \frac{1}{k}(x_i-\alpha - \frac{f''(\xi)}{2f'(x_i)}(x_i-\alpha)^2)
+x_{i+1} - \alpha &= (x_i - \alpha) - \frac{1}{k}(x_i-\alpha - \frac{f''(\xi)}{2f'(x_i)}(x_i-\alpha)^2) \\
 &= \frac{k-1}{k} (x_i-\alpha) + \frac{f''(\xi)}{2kf'(x_i)}(x_i-\alpha)^2.
 \end{align*}
 $$