See the coversheet for instructions and the point value of each problem.
- Simplify and cancel so that you can plug in the given value
without dividing by 0. Then plug in the value.
- For \(x=2\), \( \frac{x^2+x-6}{x-2}=\)
- For \(x=4\), \( \frac{\sqrt{x}-2}{x-4}=\)
- For \(h=0\), \( \frac{(x+h)^2 -x^2}{h}=\)
- For \(h=0\), \( \frac{(x+h)^{-1} - x^{-1}}{h}=\)
- For \(h=0\) and \(f(x)=2x^2\), \(\frac{f(x+h) -f(x)}{h}=\)
-
Sketch the graph of a single function \(f\) that:
- has \(\displaystyle \lim_{x\rightarrow 0}f(x)=1\)
- has \(\displaystyle \lim_{x\rightarrow 3^-}f(x)=-2\)
- has \(\displaystyle \lim_{x\rightarrow 3^+}f(x)=2\)
- has \(f(0) = -1\)
- has \(f(3) = 1\)
- A machinist is required to
manufacture a circular metal disk with area \(1000\,
\mathrm{cm}^2\).
- What radius produces such a disc?
- If the machinist is allowed an error tolerance of \(\pm
3\, \mathrm{cm}^2\) in the area of the disk, how close to the
ideal radius you found above must the machinist control the
radius?
- In terms of the \(\epsilon\), \(\delta\) definition of
\(\displaystyle \lim_{x\rightarrow a} f(x)=L\), what is
\(x\)? What is \(a\)? What is \(L\)? What value of
\(\epsilon\) is given? What is the corresponding value of
\(\delta\)?
Last modified: Tue Aug 29 14:44:25 UTC 2017