221-wainger-07spfin

# 221-wainger-07spfin - Math 221 _ Friday, May 18, 2007 Final...

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Unformatted text preview: Math 221 _ Friday, May 18, 2007 Final Exam (please print) Name: (please print) TA’s Name: Each Problem is worth 20 points. No calculators allowed. Show all work. Math 221 Page 1 1.- Find the tangent line to the curve y=3332—5x at (1,—2). Math 221 2. Find mﬂm=wmﬂ (ii) f(:1:) : V332 + 1 0053: mnﬂm=eﬂﬂ ﬁﬂﬂﬂ=£ 0+mﬂt Page 2 Math 221 Page 3 3. Evaluate the following integrals. (a) /13 513(1 + 11:2)1/2dm Math 221 Page 4 4. A particle moves along the parabola 'y = \$2 so that its x coordinate increases at a rate of 1 ft / sec. How fast is its distance to the origin changing when its x coordinate is 2 feet? Math 221 Page 5 5. A rectangle is inscribed in an isosceles right triangle with one side along the hypotenuse. The length of the hypotenuse is 2 feet. How large can the area of the rectangle be? Math 221 Page 6 6. In each case ﬁnd the maximum value of f for cc in the indicated interval (a) f(a:)=x4—2a:2, —2<x<3 (b) f(\$)=a:+\/:z:2+3 —l<x§1 Math 221 . V Page 7 7. Find the volume of the solid generated by revolving the region between the y axis and the curve a: = 2/y, 1 S y S 4 about the y—axis. Math 221 . Page 8 1 8. Find the area of the bounded region between the curves y = —, y 2: a: for which a: x32. ...
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## 221-wainger-07spfin - Math 221 _ Friday, May 18, 2007 Final...

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