Math 2260 HW #6
Due 10:10 AM Friday, February 15
Reading: Hass §8.1–8.2
Problems: Do the assignment “HW6” on WebWork. In addition, write up solutions to the
following problems and hand in your solutions in class on Friday.
1. A pot of soup is left to simmer for a long time over steady heat; as a result, the soup has
equilibrated and its temperature isn’t changing. You want to check the temperature of the
soup, so you pull out a digital thermometer. Before putting the thermometer into the soup
it reads 70◦ F, and after 1 second in the soup it reads 90◦ F. If the temperature of the soup is
actually 150◦ F, how long will it take until the thermometer reading passes 145◦ F?
2. A painting attributed to Vermeer (who lived from 1632 to 1675) suddenly appears, seemingly
out of nowhere, on lot list for an upcoming Sotheby’s auction. Skeptical art historians from
the National Gallery in London take a small sample of the paint from the painting and
determine that it contains 99.1% of its original 14 C. Is the painting authentic, or is it a
forgery? (Remember that the half-life of 14 C is 5730 years.)
3. Assuming n is a positive integer, evaluate the indefinite integral
Z
xn ln(x) dx.
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