deletions | additions       diff --git a/beginproblem_a_You_a.tex b/beginproblem_a_You_a.tex  index b69e57d..3dfec34 100644  --- a/beginproblem_a_You_a.tex  +++ b/beginproblem_a_You_a.tex 
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\begin{problem}  Prove \textbf{Problem 2: }Prove  that there is an integer $c>0$ such that the following inequality holds for all $n\ge c$:  %  \begin{equation*} 
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then prove by induction that it holds for all $n \ge c$.  \end{problem}  \begin{problem}  Give the asymptotic values of the  following functions, using the $\Theta$-notation:  %  \begin{description}  %  \item{(a)} $2n^3 + 2n^4 + n + 4120$  \item{(b)} $3n^{1.5} + 21\sqrt{n}\log n + n$  \item{(c)} $\log_5 n + \sqrt{n}+ 1/\log n$  \item{(d)} $13n^3\log n + 7n^{121} + 1.03^n$  \item{(e)} $n^33^n + 17n2^n + 4^n/n$  %  \end{description}  %  Justify your answer.  (Here, you don't need to give a complete rigorous proof.  Give only an informal explanation using asymptotic  relations between the functions $n^c$, $\log n$, and $c^n$.)  \end{problem} \textbf{Solution 2: }  To submit the homework, you need to upload the pdf file into ilearn by 8AM on Tuesday,