MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 2 Week 2

See the coversheet for instructions and the point value of each problem.

  1. Simplify and cancel so that you can plug in the given value without dividing by 0. Then plug in the value.
    1. For \(x=2\), \( \frac{x^2+x-6}{x-2}=\)
    2. For \(x=4\), \( \frac{\sqrt{x}-2}{x-4}=\)
    3. For \(h=0\), \( \frac{(x+h)^2 -x^2}{h}=\)
    4. For \(h=0\), \( \frac{(x+h)^{-1} - x^{-1}}{h}=\)
    5. For \(h=0\) and \(f(x)=2x^2\), \(\frac{f(x+h) -f(x)}{h}=\)
  2. Sketch the graph of a single function \(f\) that:
    1. has \(\displaystyle \lim_{x\rightarrow 0}f(x)=1\)
    2. has \(\displaystyle \lim_{x\rightarrow 3^-}f(x)=-2\)
    3. has \(\displaystyle \lim_{x\rightarrow 3^+}f(x)=2\)
    4. has \(f(0) = -1\)
    5. has \(f(3) = 1\)
  3. A machinist is required to manufacture a circular metal disk with area \(1000\, \mathrm{cm}^2\).
    1. What radius produces such a disc?
    2. 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?
    3. 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