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Announcements
for Section 201Please remember to staple your pages together, and print your name and student number at the top right of the first page. Show your work.
1.4(b, j, n), 1.7, 1.9, 1.10, 1.13
Note: for 1.9, the area enclosed by a frame does not count the border.
1.17, 1.19
2.3, 2.7, 2.8, 2.9, 2.12, 2.13, 2.16, 2.17
3.3, 3.4 (g,j,m,p,r) 3.5 (b,d,f,g,i), 3.9, 3.11, 3.13, 3.14, 3.16
3.19, 3.20(b)
4.1, 4.4, 4.5, 4.10, 4.12, 4.16, 4.19, 4.20, 4.23
4.25, 4.28, 4.29
5.1, 5.3, 5.5, 5.6, 5.7, 5.11, 5.13
5.15, 5.16, 5.17
6.3, 6.4(b,d,f,g,j,l,n), 6.5
E.1: Show that the function y = (ex + e-x)/2 satisfies the differential equation (y')2 + 1 = y2. What is the length of the graph of this function from x = -1 to x = 1?
E.2: Using trigonometric identities, show that cos(A) cos(B) = (cos(A+B) + cos(A-B))/2
Use this fact to find
6.7(a,b,d), 6.10(a,c,d), 6.11(d,f,g), 6.12((9),(11),(26))
E.3 Use a trigonometric substitution to find
E.4 Some more integrals:
(a) 
(hint: partial fractions)
(b) 
(hint: complete the square, then do two pieces separately)
(c) 
(hint: substitution)
7.1(a, c, d), 7.3, 7.7, 7.11, 7.14, 7.15, 7.19, 7.22
E.5 The only possible values of a certain random variable X are 0, 1 and 2, with p(0) = 1/3 and p(1) = 1/2. Find:
(a) p(2)
(b) the mean of X
(c) the standard deviation of X
8.2, 8.4, 8.10, 8.11, 8.15(a, c)
From Discrete Probability: Extra Problems: 1, 2, 4
(Note: in 2, assume the four shots are all independent. It's possible for the gun to hit the plane more than once: you're asked for the probability that it hits the plane at least once. In 4(b) you're asked for the probability that there are exactly 10 female chicks.)
E.6 A certain gene has two alleles A and a. A is dominant and a is recessive, so both AA and Aa genotypes show the A trait, while only the aa genotype shows the a trait. In a certain large population, 36% of the individuals have the A trait and 64% have the a trait. Assume random non-assortative mating, so the Hardy-Weinberg law applies.
(a) Find the gene frequencies p and q for A and a respectively.
(b) What fraction of aa individuals in this population have both parents of genotype aa?
Hint: Compute this using the probability that an individual's parents are both aa and the probability that an individual is aa.
9.1(a), 9.4, 9.5, 9.6, 9.7, 9.11, 9.14
E.7. My bathtub has a flat bottom and vertical sides, so the volume of water in it is Ah where A is the area of the bottom and h is the depth of the water. When water drains out, it does so at a rate proportional to the square root of the depth, as in section 9.5.
I start with an empty tub, stop up the drain and turn on the tap. It takes 10 minutes for the tub to fill completely (to a depth of 50 cm). Then I turn off the tap, remove the stopper, and the tub drains completely in 8 minutes. Now I turn on the tap again, but (heedless of the resulting waste of water) I leave the stopper out. The tub fills partially, approaching a constant depth as t goes to infinity. How full will the tub get?
Hint: You don't have to solve the differential equation with tap on and stopper out, just find a steady state solution.
10.2(a, c, d, f), 10.3, 10.6, 10.7, 10.9 (a, c, d, f), 10.11
10.13, 10.14, 10.17(a,c), 10.18, 10.20, 10.21, 10.23
Midterm 2 (2006 -202) (no solutions available)
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| Midterms | 30% |
| Homework | 10% |
| Labs | 10% |