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Unformatted text preview: Math 137 ASSIGNMENT 1 Fall 2007 Submit all boxed problems and all extra problems by 8:20 am. September 21.
All solutions must be clearly stated and fully justiﬁed. U se the format given on UVVACE
under Content, in the file Assignment Format for Math 135 and Math 137. NOTE : The TEXT problems without boxes are suggested for use in preparing for your
Assignments, and / or for review before tests and examinations. TEXT PROBLEMS : Section 1.1 9, i2, 16, 17, 22. 28. , , . 59, or, 68
(1 Section 1.2 8., 15, 19, '2
Section 1.3 r 4a),d) . 16. . 24, 28, , 44, 48, 51, 53, 59, 61 Appendix A 23, 25. . . 38. , .56. 57, .59, , 63, 68
EXTRA PROBLEMS: 1 El] Sketch the graph of y = 9 9 using the reciprocal method on page 16 of the Course
1. Notes.
El.2 Sketch the given function using the deﬁnition of the absolute value function and/or
grainneal operations on basic functions. a) + [1:17)2 + 1 b) (21 + 211/3 e) 1 in; — 11V2
Elil a) Solve the eqmttion l1: — 11 = 1 — :r: . b) Solve the inequality 117 — 3 < 2;rl . B14 Suppose y is the temperature in Centigrade degrees, and x is the temperature in
ralirenheit degrees. a.) Write a functional relationship y = between the two measures.
1)) Sketch y = (1(1) and y = on the same graph. Explain What is ha1')pening physically at their point of intersection. 1315* According to .1. Khufiialtl Smith (in Models in. Ecology, Oxford : Cambridge University
Press, 197/1). in population models, the size ol' the next generation in terms of the
size of the current generation can be. modelled by _ _ 1 + (a:r:)b where A, on and l) are positive constants continued... fll‘) \ ""ln‘0nglroui your assignments in Maih 137. problems marked with an >i< were adopted from problems
in Calculus with. pplicrtlinns (8th, ed.) by N1. Linl, R. Greenwell. and N. Ritehey, 2005. Pearson/Addison—
Wesley. Suppose a, = b = 1, and /\ = 3 for at certain cell population, with x and f(:t') 1)) measured in millions of cells. Show that f(J:) can be written as 1 )
1+1]:1 and hence ﬁnd the limiting size 01' the population as an increases. f(1«')= 3(1— . . . i . 1 .
Sketch a, qualitative graph 01 [ HINT: Start With y = — for .7: > 0 ; you Wlll
I need a reflection two shifts, and one scale, not necessarily in that ()1‘Ci0]'.]
Suppose instead that a = l: and b = A = 3. State the resulting model, sketch its
graph for an > U, and discuss how its predictions diflci' [I'Ul'll those of the model in
at), b). [1»11N'1‘: See Example. 7; pages 17—18 of your Course Notes for help with the
qualit ative graph .] ...
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