practice test 3

# practice test 3 - to make it Note Volume of a cone is given...

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MAT 111 Practice Test 3 No Calculators Allowed 1

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1. (25 points) Find the absolute maximum and minimum values of f on the given interval. (a) (15 points) f ( x ) = x 3 - 1 . 5 x 2 - 6 x + 1 , [ - 2 , 4] (b) (10 points) f ( x ) = x + 2 sin x, [ - π, π ] 2
2. (25 points) Suppose 2 f ( x ) 5 for all values of x . Show that 8 f (7) - f (3) 20 . 3

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3. (35 points) A cone shaped martini glass is to be made so as to hold 27 cm 3 of cocktail. Find the height and radius of the glass so that the least amount of material is needed
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Unformatted text preview: to make it. Note: Volume of a cone is given by V = 1 3 πr 2 h and surface area of cone is given by A = πr √ r 2 + h 2 . 4 4. (25 points) Find the area under the curve (i.e. evaluate the deﬁnite integral) in the given interval for the following functions. (a) (15 points) f ( x ) = 2 cos 2 x + sin x, [-π/ 4 , π/ 4]. (b) (10 points) f ( x ) = x 2 + sec 2 x, [0 , π/ 3]. 5...
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