practice test final

# practice test final - MAT 111 Practice Final No Calculators...

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MAT 111 Practice Final No Calculators Allowed Spring 2010 1

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1. (20 points) Find the following limits: (a) lim x →∞ sin 2 x x 2 (b) lim t 0 sin 2 3 t t 2 2
(c) lim x 0 + x [1 + sin 2 (2 /x )] (d) lim h 0 1+ h - 1 h 3

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2. (10 points) Differentiate the following. (a) y = ( x 2 + 2) 1 + tan x (b) y = tan x +2 sin 2 x 4
3. (20 points) A boat is pulled into a dock by a rope attached to the bow of the boat and the passing through a pulley on the dock that is 6 feet higher than the bow of the boat. If the rope is being pulled in at 4 ft/s, how fast is the boat approching the dock when it is 8 ft away from the dock. 5

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4. ( 15 points) When a spherical snowball starts rolling down a snowy slope, it’s surface area increases at 3 cm 2 /s . How fast is the volume of the snowball increasing when

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Unformatted text preview: it’s diameter is 10 cm. 6 5. (15 points) At which points on the curve y = 1 + 40 x 3-3 x 5 does the tangent line have the largest slope ? 7 6. (20 points) A planet J has a moon E rotating around it in an elliptical orbit. If the planet is assumed to be located at (2 √ 3 , 0), the moon follows the orbit given by x 2 16 + y 2 4 = 1. What is the distance between the moon and the planet when they are closest to each other ? 8 7. (10 points) Find the area under the curve (i.e. evaluate the deﬁnite integral) in the given interval for f ( x ) = sec x (sec x + tan x ) , [0 , π/ 3]. 9...
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