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221-wainger-07sp02

221-wainger-07sp02 - Math 221 Thursday Midterm Exam L...

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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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221-wainger-07sp02 - Math 221 Thursday Midterm Exam L...

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