posted solutions of 2 and 3 in pset2

1 files changed, 4 insertions, 4 deletions

diff --git a/Problem Set 2.page b/Problem Set 2.page
index 3f1a214..078d5e1 100644
--- a/Problem Set 2.page
+++ b/Problem Set 2.page
@@ -40,8 +40,8 @@ $\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$
 
 2. Since
 $\sin x = \frac{e^{ix}-e^{-ix}}{2}$,
-$ \sin^4 x = \frac{{( e^{ix}-e^{-ix} )}^4}{16}$,
-$ = \frac{e^{i 4x}+e^{-i 4x}-4 e^{i 2x} -4 e^{-i 2x}+6}{16}$.
+$\sin^4 x = \frac{{( e^{ix}-e^{-ix} )}^4}{16}$,
+$= \frac{e^{i 4x}+e^{-i 4x}-4 e^{i 2x} -4 e^{-i 2x}+6}{16}$.
 
 If we express any periodic function $f(x)$ as 
 
@@ -54,9 +54,9 @@ $a_{-4} = a_{4} = \sqrt{2\pi} \times 1/16$, $a_{-2} = a_{2} = - \sqrt{2\pi} \tim
 
 
 Since $a_m = < f_m, f >$,
-$ \int_0^{2\pi} \sin^4(x) dx = <1, f> = \sqrt{2\pi} \times <f_0, f>$
+$\int_0^{2\pi} \sin^4(x) dx = <1, f> = \sqrt{2\pi} \times <f_0, f>$
 
-$ = \sqrt{2\pi} \times a_0 = \frac{3 \pi}{4}$
+$= \sqrt{2\pi} \times a_0 = \frac{3 \pi}{4}$
 
 
 ## Cardinality