This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 xaxis. 0) Give the end points in polar coordinates. 10. Sketch the polar curve: r(6) = —2 cos(3x) ...
View
Full Document
 Spring '06
 Sarason
 Calculus

Click to edit the document details