Math 151 WIR Spring 2010 c Benjamin Aurispa Math 151 Week in Review 7 Sections 3 8 3 9 3 10 1 Find f 00 x for f x x x2 3 2 Find f 53 x for f x cos x7 3 Find a formula for f n x where f x 1 and a is some constant ax 1 2 1 Math 151 WIR Spring 2010 c Benjamin Aurispa 4 If the position of an object in linear motion is given by s t the points where the velocity is 0 t3 3t2 8 find the acceleration at 5 Given the position function r t 4 cos 2t cos2 t find the acceleration when t 2 2 Math 151 WIR Spring 2010 c Benjamin Aurispa 6 Consider the curve x t2 10t 3 y 5t2 t a Find the equation of the tangent line at the point 8 4 b At what point s is the tangent line to the graph parallel to the line 7x 2y 19 7 Find an equation of the tangent line to the curve x 8 sin2 t y 4 cos 2t when t 3 3 Math 151 WIR Spring 2010 c Benjamin Aurispa 8 Find the points on the curve x t3 9t2 y 2t3 3t2 12t where the tangent line is horizontal or vertical 9 The curve x t3 9t y t2 5 crosses itself at the point 0 4 Find the equations of both tangent lines at this point 4 Math 151 WIR Spring 2010 c Benjamin Aurispa 10 A spherical balloon is being inflated so that its diameter is increasing at a rate of 3 in s How fast is the volume of the ballon increasing when the diameter is 10 inches 11 A man watches a rocket launch from a distance of 150 m When the rocket is at a height of 200 m it is rising vertically with a speed of 300 m s a At what rate is the angle of elevation from the man to the rocket changing at this instant 5 Math 151 WIR Spring 2010 c Benjamin Aurispa b At what rate is the distance from the man to the rocket changing at this instant c If the man runs toward the launch pad at a rate of 2 m s and the rocket continues rising at 300 m s how fast is the distance between them changing 5 seconds later 6 Math 151 WIR Spring 2010 c Benjamin Aurispa 12 An inverted circular cone with radius 20 ft and height 30 ft is being filled with water at a constant rate If the water level is rising at a rate of 3 ft s when the height of the water is 4 ft at what rate is the water being poured in 13 A trapezoid has a base with length 10 inches The length of the top of the trapezoid is decreasing at a rate of 1 in min while the height of the trapezoid is increasing at a rate of 2 in min At what rate is the area of the trapezoid changing when the height is 3 inches and the area of the trapezoid is 24 in2 7 Math 151 WIR Spring 2010 c Benjamin Aurispa 14 A trough has ends which are equilateral triangles with side length 6 cm The length of the trough is 30 cm If water is being poured into the trough at a rate of 50 cm3 hr at what rate is the water level rising when the height of the water is 2 cm 8
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