ana7 done, fixed all bad breaks and overfull boxes

ana1.tex

@@ -32,8 +32,8 @@
             $x=0$: $f_n(0) = 0 = f(0)$\\
             $0 < x \le 2$: $\forall n \ge \frac{2}{x}$, $f_n(x) = 0 = f(x)$
         \item $f_n(x) = x^{n}$, $f_n\colon [0,1] \to \R$.
-            \begin{figure}[h!]
-                \begin{tikzpicture}
+            \begin{figure}[ht!]
+                \begin{tikzpicture}[scale = 0.97]
                     \begin{axis}%
                         [grid=both,
                          minor tick num=4,
@@ -50,7 +50,7 @@
                         \addplot[domain=0:1,samples=50,smooth,red] {x^4};
                       \end{axis}
                 \end{tikzpicture}
-                \begin{tikzpicture}
+                \begin{tikzpicture}[scale = 0.97]
                     \begin{axis}%
                         [grid=both,
                          minor tick num=4,
@@ -95,8 +95,8 @@
         \text{graph}(f_n) \subset \epsilon\text{-Umgebung von Graphen von } f
         := \{ (x, y) \in D \times \R  \mid | y - f(x)| < \epsilon\} 
     .\] 
-    \begin{figure}[h!]
-        \begin{tikzpicture}
+    \begin{figure}[ht!]
+        \begin{tikzpicture}[scale = 0.97]
             \begin{axis}%
                 [grid=both,
                  minor tick num=4,
@@ -113,7 +113,7 @@
                 \addplot[domain=0:1,samples=50,smooth,dashed, blue] {0.3*sin(deg(8*x)) + 0.2*x + 0.3};
               \end{axis}
         \end{tikzpicture}
-        \begin{tikzpicture}
+        \begin{tikzpicture}[scale = 0.97]
             \begin{axis}%
                 [grid=both,
                  minor tick num=4,
@@ -293,10 +293,12 @@ Wichtige Frage: Wenn $f_n \to f$, gilt dann auch $\int_{a}^{b} f_n \to \int_{a}^
     $f_n \xrightarrow[\text{gleichmäßig}]{n \to \infty} f \implies f$ stetig $\implies f$ Riemann-integrierbar.
 
     Es gilt
-    \[
-        \left| \int_{a}^{b} f_n(x) dx - \int_{a}^{b} f(x) dx\right| = \left| \int_{a}^{b} (f_n(x) - f(x))dx\right|   
-        \le \int_{a}^{b} |f_n(x) - f(x)| dx \le \underbrace{\max_{x \in [a,b]} |f_n(x) - f(x)|}_{= \underbrace{\Vert f_n - f \Vert_\infty}_{\xrightarrow{n \to \infty} 0}\underbrace{(b-a)}_{\text{beschränkt}}}
-    .\] 
+    \begin{align*}
+        \left| \int_{a}^{b} f_n(x) dx - \int_{a}^{b} f(x) dx\right| &= \left| \int_{a}^{b} (f_n(x) - f(x))dx\right|\\
+        &\le \int_{a}^{b} |f_n(x) - f(x)| dx\\
+        &\le \max_{x \in [a,b]} |f_n(x) - f(x)| \cdot (a-b)\\
+        &=\underbrace{\norm{f_n - f}_\infty}_{\xrightarrow{n \to \infty} 0}\underbrace{(b-a)}_{\text{beschränkt}}.
+    \end{align*}
 \end{proof}
 
 \begin{satz}\label{permutesumint}