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21b_final

# 21b_final - 21B ~ Sara’s Practice F inal 1 You have 10...

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Unformatted text preview: 21B ~ Sara’s Practice F inal 1. You have 10 pounds of radioactive isotope A and 40 pounds of isotope B. If the half life of A is 60 months and the half life of B is 24 months, when will you have the same amount of the two isotopes? 2. a) What is the maximum value of :x—Zcos(x)l ? b) Give an upper bound on the error if we use trapezoid rule to estimate [17003de with n=3 4 c) If we want the error to be no more than 10‘6 what should n be? 3. Solve, %=y2 +yzex if x0 #- 0, y0 =3 Integrate. . . a).[iﬁhk 2 2 b) 6x2+3 dx x(x +1) l 5 3x dx Hint: u =u4—2u3+4u2—8u+16— 32 C ) J15” u+2 u+2 a) What condition must be placed on p so that the following integral converges? J —pdx 1 x °° 3 b) Show that J W—dx converges. 1 sz + 2 . Converge or diverge? If it converges, evaluate. a)J 2 dx 0 ex+3 b) I: ln(x) dx *show your work on the limit! 7. Consider the region bounded by: y = x2 , x = 0 , and y = 2 — x2 . a) SET UP and integral to ﬁnd the volume if this region is revolved around x = —5 b) If this region is a plate with density given by 6 (x) = 2x SET UP integrals to ﬁnd the center of mass. 8. A giant spring is stretched 2m beyond its relaxed length. If 42] of work are needed to pull it another 3m, how much force is required to hold it there? 7. Consider the region bounded by: y = x2 , x = 0 , and y = 2 — x2. a) SET UP and integral to ﬁnd the volume if this region is revolved around x = —5 b) If this region is a plate with density given by 6(x) = 2x SET UP integrals to ﬁnd the center of mass. 8. A giant spring is stretched 2m beyond its relaxed length. If 42] of work are needed to pull it another 3m, how much force is required to hold it there? 9. Consider the portion of y = V9 - x2 from ls x S 3. a) SET UP an integral to ﬁnd the length of this curve b) SET UP an integral to ﬁnd the surface area if this curve is rotated around the x-axis. 0) Give the end points in polar coordinates. 10. Sketch the polar curve: r(6) = —2 cos(3x) ...
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21b_final - 21B ~ Sara’s Practice F inal 1 You have 10...

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