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151 WebCalc Fall 2002-copyright Joe Kahlig
Quiz #17
MATH 151 Section
Name:
November 5, 2002
Show all your work. This is due at the start of class on Thursday.
1. The air in a factory is being filtered so that the quantity of pollutant, P (measured in mg/liter),
is decreasing at a rate that is proportional to the amount left. This means it is decreasing
exponentially. If 10% is removed in the first 5 hours, find a formula that gives the percentage
of the pollution that is remaining as a function of time.
2. Simplify the following. Give exact values. Do not give decimal approximations.
(a) cos(arcsin(x + 2)) =
(b) tan−1 (tan 5π
3 )=
3. Find the derivatives of the following functions.
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(a) y = sin−1 (3x)
(b) y = xsec
−1 (x)
(c) y = arctan(sin(4x))