Calculus I :: Lab 02

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Let \(\displaystyle f(x) = \frac{4|x-1|}{x-1}\).

1. Graph \(f(x)\).
2. Find all discontinuities of \(f\).
3. Classify each discontinuity as one of "removable", "jump", "infinite", or "other". You should justify your answer using tables to show limit values.

Repeat Problem 1 with \(\displaystyle g(x) = \frac{x^2+x-6}{x^2-4}\).

Repeat Problem 1 with \(\displaystyle h(x) = \frac{\sqrt{x} -2}{x-4}\).

Repeat Problem 1 with \(\displaystyle i(x) = \frac{e^x}{\cos x}\) where \(i\) has domain \([0,2\pi]\).

Repeat Problem 1 with

\begin{equation*} j(x) = \begin{cases} x & x \leq 1 \\ x^2 & 1 < x \leq 3 \\ \sqrt{x} & 3 < x. \end{cases} \end{equation*}

Let

\begin{equation*} k(x) = \begin{cases} x + 4 & x \leq 0 \\ (c-x)^2 & 0 < x \end{cases}. \end{equation*}

Find the value of \(c\) which makes \(k\) continuous everywhere, and graph this continuous function.