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Commit8333d117c5d0e24da79b1ae93ac8f824140fd15e (patch)
Author
 Syndamia <kamen.d.mladenov@protonmail.com>
2022-01-29 09:00:16 +0200
Committer
 Syndamia <kamen.d.mladenov@protonmail.com>
2022-01-29 09:00:16 +0200
Filesba201f9b66f8292a4fe0330d4ad2494b01f02ca9 /Year 1/Calculus/Homeworks/Homework3.tex
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Parentc2575a1f3ef10524b0938114b6d0ad309cf40041 (diff)
Added grade for dis hw3
1 files changed, 10 insertions, 5 deletions
-rw-r--r--Year 1/Calculus/Homeworks/Homework3.tex15
diff --git a/Year 1/Calculus/Homeworks/Homework3.tex b/Year 1/Calculus/Homeworks/Homework3.tex
index bf93382..60460f0 100644
--- a/Year 1/Calculus/Homeworks/Homework3.tex
+++ b/Year 1/Calculus/Homeworks/Homework3.tex
@@ -44,9 +44,12 @@
\maketitle
+\noindent
+\colorbox{Dandelion}{\parbox{\textwidth}{\; Отличен 5,10/6 \qquad [Коментарите са под определените места]}}
+
\paragraph{\colorbox{yellow}{Задача 1.}}
-Пресметнете границата
+Пресметнете границата \hfill \colorbox{YellowGreen}{0,8/0,8 т.}
\begin{align*}
\lim_{x \rightarrow 0} \frac{\ln (x^2+1) - 3e^x + \sqrt[4]{12x + 1} + 2}{\tg(x^2) - 1 + \cos x}.
\end{align*}
@@ -67,7 +70,7 @@
\paragraph{\colorbox{yellow}{Задача 2.}}
-Да се развие по формулата на Маклорен с точност до $o(x^{2n})$ функцията
+Да се развие по формулата на Маклорен с точност до $o(x^{2n})$ функцията \hfill \colorbox{Dandelion}{0,7/0,8 т.}
\begin{align*}
f(x) = (x^2-1) \cos 2x + \ln (3 - 6x^2)
\end{align*}
@@ -82,12 +85,14 @@
\end{align*}
\begin{align*}
f(x) & = \ln 3 - \sum_{k = 2}^n \frac{2^kx^{2k}}{k} - \cancel{2x^2} - 1 + \cancel{2x^2} + \sum_{k = 2}^n \left( \frac{(-4)^{k-2} x^{2k-2}}{(2k-4)!} - \frac{(-4)^k x^{2k}}{(2k)!} \right) + o(x^{2n}) = \\
- & = \answerbox{\ln 3 - 1 + \sum_{k = 2}^n \left( \frac{(-4)^{k-2} x^{2k-2}}{(2k-4)!} - \frac{(-4)^k x^{2k}}{(2k)!} - \frac{2^kx^{2k}}{k} \right) + o(x^{2n})}
+ & = \answerbox{\ln 3 - 1 + \sum_{k = 2}^n \left( \frac{(-4)^{k-2} x^{2k-2}}{(2k-4)!} - \frac{(-4)^k x^{2k}}{(2k)!} - \frac{2^kx^{2k}}{k} \right) + o(x^{2n})} \quad \colorbox{RedOrange}{$x^{2k}$ да се изведе пред скоби}
\end{align*}
+\paragraph{\colorbox{yellow}{Задача 3.}} \hfill \colorbox{RedOrange}{0,0/0,8 т.}
+
\paragraph{\colorbox{yellow}{Задача 4.}}
-Изследвайте функцията и начертайте графиката и:
+Изследвайте функцията и начертайте графиката и: \hfill \colorbox{YellowGreen}{0,8/0,8 т.}
\begin{align*}
f(x) = \frac{x - 1}{\sqrt{1 + x^2}}
\end{align*}
@@ -141,7 +146,7 @@
\paragraph{\colorbox{yellow}{Задача 5.}}
-Пресметнете интеграла
+Пресметнете интеграла \hfill \colorbox{YellowGreen}{0,8/0,8 т.}
\begin{align*}
\int x \arctg(x^2) \D x
\end{align*}