ptest2B - half of a sphere Assuming that the radius of the...

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Name: Practice Test 2B for Test 2 (MTH 151K) 1. Evaluate y : (a) y = sin(ln x ). (b) y = t 3 ln t . (c) y = x x . (d) y = r ( x 2 + 1)( x - 1) 2 . 2. Find y : (a) y = (arctan x ) 2 . (b) y = arcsin( e x ). (c) y = arccos(1 /x ). 3. Prove the following di±erentiation formula: d dx [arctan x ] = 1 1 + x 2 . 4. A particle moves along the parabola y = x 2 in the ²rst quadrant in such a way that its x -coordinate increases at a steady 10 meters per second. How fast is the angle of inclination θ of the line joining the particle to the origin changing when x = 3 meters? 5. A coat of paint .001 meters thick is to be applied to a dome, which has the shape of
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Unformatted text preview: half of a sphere. Assuming that the radius of the dome is 10 meters, use di±erentials to estimate the amount of paint that will be required. (You should use the fact that the volume of a sphere is given by the equation V = 4 3 πr 3 . ) 6. Find the maximum and minimum values of the function on the given interval: f ( x ) = x 2-1; [-1 , 2] . 7. Show that the equation x 3 + x + 3 = 0 has at most one solution....
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