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151 WebCalc Fall 2002-copyright Joe Kahlig
In Class Questions
MATH 151-Fall 02
November 5
1. A picture supposedly painted by Vermeer (1632-1675) contains 99.5% of its carbon-14 (half life
of 5730 years). From this information, can you decide whether or not the picture is a fake?
Explain your reasoning.
2. A tank contains 100L of brine with a concentration of 0.2 kg of salt per liter. Pure water enters
the tank at a rate of 10 L/min and the resulting solution, which is stirred contnuously, runs out
at the same rate.
(a) How many kilograms of salt remain after half an hour?
(b) When will the concentration reach 0.15 kg/L?
3. Find the exact expression.
5π
4
5π
(b) arccos cos
4
7π
(c) arctan tan
4
2
(d) sec arctan
3
(a) arcsin sin
(e) sin(2 cos−1 x)
4. Take the derivatives of the following.
(a) y = 4 arcsin(7 − x)
(b) y = arccos(4x2 )
(c) y = x3 tan−1 (3x)
(d) y = cot−1 (e2x )