MATH 2301-100 Spring 2022 Calculus I Recitation 8 Week 11

Work in a group of at most 4. Explain to those who do not understand. Ask questions if you do not understand.

  1. (10 points) Use differentials to approximate the value of \(\sqrt[3]{26.8}\) by hand.
  2. (10 points) What is the propagated error in the measurement of the cross sectional area of a circular log if the diameter is measured at 24 cm, accurate to 0.2 cm?
  3. (20 points) Find each of the antiderivatives. (Remember the "\(+C\)"!)
    1. \(\int 2\,dx=\)
    2. \(\int x^2 \,dx=\)
    3. \(\int \frac{1}{x^2}\,dx=\)
    4. \(\int \frac{1}{x}\,dx=\)
    5. \(\int x^{1/2}\,dx=\)
    6. \(\int \cos(x)\,dx=\)
    7. \(\int \cos(7)\,dx=\)
    8. \(\int e^x\,dx=\)
    9. \(\int x^2+1\,dx=\)
    10. \(\int \frac{1}{x^2+1}\,dx=\)
  4. (10 points) Find the function \(f(\theta)\) that has \(f''(\theta)=\sin(\theta)\), \(f'(\pi)=6\), and \(f(\pi)=5\).
  5. (25 points) For the function \(\displaystyle f(x)= \frac{x-1}{x}\):
    1. Find any vertical asymptotes.
    2. Find any horizontal asymptotes.
    3. Find the intervals on which \(f\) is increasing or decreasing.
    4. Find the local maximum and minimum values of \(f\).
    5. Find the intervals of concavity and the inflection points.
    6. Use the information above to sketch the graph.
  6. (25 points) A cone-shaped drinking cup is made from a circular piece of paper of radius \(5\,\mathrm{in}\) by cutting out a sector and joining the edges \(CA\) and \(CB\). Find the maximum capacity of such a cup. water cone

Last modified: Fri Mar 25 18:25:31 UTC 2022