## lab

lab. lab.

1. Find the length of the curve for.  Hint: Use  and
2. Show that the arc length is independent of the functions below that parameterize the curve. Compute the length of the semicircle   of radius 1 and center at (0,0) by using the two different parametric equations of the circle given below and show that the arc length is the same.   This argument suggests that ark length is independent of parameterization; though, it is not a proof of it as we would need to show that this holds for all parameterizations.
3. where
4. where
5. Find the length of the Arc of St. Louis, if the equation used in construction the arc is  where
6. Find the center of mass of the trapezoid with constant density 1 and with vertices at (0, 0), (c, 0), (c, b), and (0, a) where a, b, and c are constants. Draw the trapezoid on the plane provided and show it is the intersection of the line connecting the midpoint of the parallel sides and the line connecting the extended parallel sides.
7. Find the center of mass of the region bounded by the graphs of and .  Assume the density is constant and is equals to 1.  Make a sketch of the region and identify its center of mass.
8. An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet.  Find S, the surface area of the bulb.
9. Find the surface area generated by revolving the curve f: [1,5] where   around the x-axis.
10. Use the theorem of Pappus to find the volume generated by revolving about the line the triangular region bounded by the coordinate axis and the line.
11. Curves represented by the graphs of the equation    are called astroids because of their shapes which look like stars.
1. Show that the graph represented by this equation is symmetric with respect to the y-axis as well as with respect to the x-axis.
2. Find the length of the astroid. Hint : Find the length of half of the first quadrant portion  using   the function      ;      x    and then multiply by 2 and use a)
3. Find the area of the surface generated by revolving the portion of the astroid represented by the graph above the x-axis. Hint: Revolve the graph in the first quadrant about the x-axis and double it.
12. Gabriel’s horn:
13. Compute volume obtained by revolvingaround x-axis for
14. Compute surface obtained by revolvingaround x-axis forP(5.u)

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lab

lab

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put all these pages into a booklet thing (like have a title page then the work after it)

P(3)

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## Hypotheses of the Mean Value Theorem

Hypotheses of the Mean Value Theorem. Hypotheses of the Mean Value Theorem. Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e^(−3x), [0, 3]

If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

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Hypotheses of the Mean Value Theorem

Hypotheses of the Mean Value Theorem

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## A random or accidental error

A random or accidental error. A random or accidental error. A random or accidental error of +/-0.007 ft is estimated for each of the 24 length measurements. These measurements are to be added together to obtain the total length.

Solution

1. What is the estimated total error?(Ans:+/-0.034 ft)-
2. What is the estimated total error if the random error is estimated to be +/-0.004 ft per length? (Ans:+/-0.020ft)

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A random or accidental error

A random or accidental error

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## Solving the Horizontal Distance

Solving the Horizontal Distance. Solving the Horizontal Distance. The slope distances shown were measured with an EDM while the differences in elevation between the ends of each line were determined by leveling. What are the horizontal distances?

Slope Distance (ft)      Elevation difference (ft)

A.    734.78             -26.54                                      (Ans: 734.30 ft)

B.     1382.81           -21.68                                      (Ans: 1382.64 ft)

C.

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972.11             +15.32                                     (Ans: 971.99 ft)

Solving the Horizontal Distance

Solving the Horizontal Distance

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