University:
Whitman College
Course:
MATH-126 | Calculus II
Academic year:

2015
Views:

95

Pages:

4
Author:

Sanaa Tate

KEY Math 126: Quiz 6 December 9, 2015 You have the remainder of the hour to complete this closed-book, closed-notes, closed-colleague quiz. You may use a calculator for arithmetic only (ie, no plotting). PLEASE READ ALL DIRECTIONS CAREFULLY! 1. Find the length of the curve y = 3 + 2z) from (1,5) to (4, 19) = 7"93"1." = 4{37-2"7 2. (a) Find the area of the surface generated by rotating the portion of the curve y - 2' between 1 = 0 and I - 3 about the r-axis. 5.1. = Saands * 5.20 2' 1329 de = S2ox Magerde $ 19(0)": / +1 = 1+ 9(3) - 730 → SA: 26 (b) Set up, but don't evaluate, the integral for the surface area generated by rotating that same portion of the curve about the y-axis. or 3. Find the value, if it exists, of e"du lim 6-100 du=-2+dy 2 6-100 te"] = 0*2 = 2 4. Without calculating, would you expect 5/2 to converge or diverge, and why? Drege. It behaves like a pinkyal w.h p= 12«1. 5. Suppose that we have society that elects 1200 new members each year. In addition, the society loses 15% of its members each year. (a) Give a differential equation for the membership M as it changes relative to time t. dM = 1200-, 15M dt M= 8000+ Be''t :: 15 (M -8000) d t (b) If there are 3000 members to begin with, how many will there be after 3 years? MCO) = 2000 = B = 8000-8000 = 5000 M= 8000-5000 € : ist M13) = 8000-5000 € 45 = 4811 (c) If there are 3000 members to begin with, how many will be in the society long-term? lany ter → 8000 as the constant Deps off (d) If there are 10,000 members to begin with, how many will there be in the society long-term? 10000 stent BLt) = 8000 +2000 € 156 → B → 8000 sh/l 6. A pair of species exist on an island and are competing for the same limited (but renewable) resource for survival. The differential equations governing the system are as follows. dA =TA+ siA?+ tAB dt d.B - = rzB + s2B? + bAB dt Are the constants (1, 51, t1, 72, 82, tz) positive or negative? Explain your rea- soning biologically. r, re 70 → These follow a lays tie pattem. to ta <0 = Whenbospecies ane present. it adversely affects botrpoplations! 7. Which concepts are you most comfortable about heading into the final? Where do you need the most work?

Calculus II Quiz 6 - Answer Key

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