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\title{\bf Assignment 1 \\[2ex]
\rm\normalsize CS 350 \\ Due: October 9, 2019}
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        Your solutions must be typed (preferably typeset in \LaTeX ) and submitted as a hard-copy at the beginning of class on the day its due.
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\paragraph{Problem 1: [10 points]}
List the functions below from lowest order of growth to highest. If any two or more are
the same, indicate which.
\begin{align*}
	&\sqrt{n} & &m & &2^n \\
	&n \log n & &n - n^3 + 7n^5 & &k^2 + \log k \\
	&m^2 &  &n^3 & &\log n \\
	&n^{\frac13} + \log n & &(\log n)^2 & &n! \\
	&\ln m & &\frac{n}{\log n} & &\log \log k \\
	&(\frac13)^n & &(\frac32)^n & &6
\end{align*}

\paragraph{Problem 2: [10 points]}
Suppose that $f(n)$ and $g(n)$ are non-negative functions. Prove or disprove the following: if $f(n) \in O(g(n))$ then $2^{f(n)} \in O(2^{g(n)})$.

\paragraph{Problem 3: [10 points]}
Prove that for any {\em positive} integer constants $a$ and $b$.
\[ (n+a)^b \in \Theta(n^b) \]
You will need to show that $(n+a)^b \in \Omega(n^b)$ and that $(n+a)^b \in O(n^b)$. (Warning: do not trust the internet's answer for this question.)

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