Differential Calculus

Rate of Change of Volume of Sand in Conical Shape

Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A.   2π ft/min C.   3π ft/min
B.   4π ft/min D.   5π ft/min

 

Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

A.   2 C.   4
B.   -2 D.   -4

 

Equation of the Diameter of Parabola Bisecting Parallel Chords of Given Slope

Problem
A parabola has an equation of y2 = 8x. Find the equation of the diameter of the parabola, which bisect chords parallel to the line xy = 4.

A.   y = 2 C.   y = 4
B.   y = 3 D.   y = 1

 

Slope of a Curve of Given Parametric Equations

Problem
A point moves in the plane according to equations x = t2 + 2t and y = 2t3 - 6t. Find dy/dx when t = 0, 2, 5.

A.   -3, -3, -12 C.   3, 3, 12
B.   3, -3, 12 D.   -3, 3, 12

 

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