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\lhead{\bf Advanced Calculus (MAA 4212)}
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\rhead{Due Wednesday 1/16}
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\Problem Suppose that $f\st X\to Y$ is uniformly continuous and that $(a_n)$ is a Cauchy sequence from $X$. Prove that the sequence $(f(a_n))$ is Cauchy in $Y$.

\Problem Prove the \textbf{Intermediate Value Theorem}: If the function $f\st [a,b]\to\mathbb{R}$ is continuous, then it takes on every value between $f(a)$ and $f(b)$ at some point within the interval $[a,b]$. (In other words, for every value $y$ between $f(a)$ and $f(b)$, there is some point $x\in[a,b]$ such that $f(x)=y$.)

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