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Unformatted text preview: Math 221 Thursday, April 19, 2007
Midterm Exam L .  7 (please print) Name: (please print) TA’s Name: Each Problem is worth 20 points.
No calculators allowed. ShOW all work. PROBLEM Math 221  V Page 1 1. Sketch thevcurve
y = f(:z:) : ~x4 +8902 —4. List all
(1) local maximum and minimum points.
(ii) inﬂection points. (iii) indicate Where f is increasing and where f is decreasing. (iv) indicate where the graph of f is concave up (convex) and Where the graph is concave down (concave). (v) draw a sketch of the curve. Math 221 . ' ‘ Page 2 2. Water is being pumped into a conical vessel at a rate of 1 cu ft / sec. 'The radius
of the top of the cone is 6 ft and the height of the cone is 8 ft. How fast is the
radius of the top of the water changing when the height of the water is 4 ft? (You are being asked for 511% when h(t) = 4.) h(t) The volume of a cone is éwﬂh. Math 221 Page 3
3, Evaluate the integrals
‘ 5 I 2 ' .
1 2 315
(a) _/3 (“2’75 + d7: (4 points)
2 t2
(b) /1 m<1+t3)1/2dt I (7 points) 7r/2 .
(c) A costsintx/ 1 + 4(sin t)2dt (9 POintS> Math 221 ' ‘ Page 4 4. Find the area of the region in the ﬁrst quadrant bounded by the curve y 2 ﬂ, the line y = 2 — x and the :c— axis.  Math 221 _ V Page 5 5. The bounded region in the ﬁrst quadrant bounded by \E and $322 is rotated around the y —axis’. Find the volume. ...
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This note was uploaded on 08/08/2008 for the course MATH 221 taught by Professor Denissou during the Summer '07 term at Wisconsin.
 Summer '07
 Denissou
 Calculus, Geometry

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