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TAMU MATH 151 - 151wir7ws

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Math 151 WIR, Spring 2010,cBenjamin 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,cBenjamin 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,cBenjamin 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,cBenjamin 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,cBenjamin 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,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 300m/s, how fast is the distance between them changing 5 seconds later?6Math 151 WIR, Spring 2010,cBenjamin 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,cBenjamin 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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