Unformatted text preview: l\/Iath 137 ASSIGNMENT 9 Fall 2007 Submit all boxed problems and all extra problems by 8:20 am. November 30.
All solutions must be clearly stated and fully justiﬁed. Use the format given on UVVACE
under Content, in the file Assignment Format for Math 135 and Math 137. ' TEXT PROBLEMS: Section 4.9 — 9, IE, I, I, I, 21, I, I, I, 39, I, 49, 52, 53, I,
Section 5.2 — 5, 19, 23, 30, I, <10, 47, I, I,
Section 5.3 — 3 , I, I, 9, 17, I, 35, I, 40, I, 51 Section 5.5 — 3, I, I 11, 141, I, 21 ,I, 25, I, 30, I, I, 40, 43, I 59, I,
I, 75 EXTRA PROBLEMS: E9.1 As you drive down a country road late one night, your headlights pick out a skunk in
your path, 200 metres ahead. You hit the brakes, hoping for the best. If the table
below gives your velocity every 2 seconds before the car stops 10 seconds later, will
you hit the skunk, or not? Suggestion: Assume v(t) is a line segment on each interval,
and hence estimate the total distance travelled using the Trapezoid Rule. E92 a) Make two sketches of the graph of y = f(m) = 2 + cos 2: for O S a; g 27r, and
illustrate £14 on one and R; on the other (the left and right Riemann sums with
4 subdivisions). ' b) Use areas to compare the values of the following quantities: R4, L4 and ~27r
/ (2 + cos (13)d:131
0 E93 Use the known error bounds for the Mid—Point Rule (ll/In) and Simpson’s Rule in these
problems. 1
a) Show that the error in approximating / f($)d23 using Mn for any function
0 f(:r) = (1er + bcc + 0 depends only on a and n. b
b) Show that Simpson’s Rule gives the exact value of / f(m)da: for any function
. Ll
f(:l:) = 1m"3 + cx‘o‘ + £11 + e. ...
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