Math 151 WIR, Spring 2010,cBenjamin AurispaMath 151 Week in Review 7Sections 3.8, 3.9, & 3.101. Find f00(x) for f(x) =xx2+ 3.2. Find f(53)(x) for f(x) = cosx73. Find a formula for f(n)(x) where f(x) =1(ax − 1)2and a is some constant.1Math 151 WIR, Spring 2010,cBenjamin Aurispa4. If the position of an object in linear motion is given by s(t) =√t3− 3t2+ 8, find the acceleration atthe points where the velocity is 0.5. Given the position function r(t) =< −4 cos 2t, cos2t >, find the acceleration when t =π2.2Math 151 WIR, Spring 2010,cBenjamin Aurispa6. 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 sin2t, y = 4 cos 2t when t =π3.3Math 151 WIR, Spring 2010,cBenjamin Aurispa8. Find the points on the curve x = t3− 9t2, y = 2t3+ 3t2− 12t where the tangent line is horizontal orvertical.9. The curve x = t3− 9t, y = t2− 5 crosses itself at the point (0, 4). Find the equations of both tangentlines at this point.4Math 151 WIR, Spring 2010,cBenjamin Aurispa10. A spherical balloon is being inflated so that its diameter is increasing at a rate of 3 in./s. How fast isthe 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 itis 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?5Math 151 WIR, Spring 2010,cBenjamin 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 300m/s, how fast is the distance between them changing 5 seconds later?6Math 151 WIR, Spring 2010,cBenjamin Aurispa12. An inverted circular cone with radius 20 ft and height 30 ft is being filled with water at a constantrate. 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 isthe water being poured in?13. A trapezoid has a base with length 10 inches. The length of the top of the trapezoid is decreasing ata rate of 1 in/min while the height of the trapezoid is increasing at a rate of 2 in/min. At what rate isthe area of the trapezoid changing when the height is 3 inches and the area of the trapezoid is 24 in2.7Math 151 WIR, Spring 2010,cBenjamin Aurispa14. A trough has ends which are equilateral triangles with side length 6 cm. The length of the trough is30 cm. If water is being poured into the trough at a rate of 50 cm3/hr, at what rate is the water levelrising when the height of the water is 2
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