Unformatted text preview: MATA26Y Physical Sciences Division
University of Toronto at Scarborough February 3, 1999
110 minutes TERM TEST II 1. Sketch the graph of f(:v) = 11:26” . 2. Two towns on opposite sides of a river want to be joined by a telephone line. The river is perfectly straight and 1 km wide. One town is exactly 3 km upstream
from the other. Suppose laying underwater telephone cable costs $100,000 per
km but laying cable on dry land costs only $50,000 per km. What will be the least expensive route for the cable? . Evaluate the following integrals: (EU/«5111mm (d) /f\j:%dx (b) ¢1$—_—$2 d$ (e) /_13 |$3 — $|d$
(w/;:;m . Describe how many subdivisions n (into equal subintervals) you would use to approximate within 10—5 the integral 2 d3:
1 3+2a: using (a) the trapezoid rule and (b) Simpson’s rule.
(Do not work out the approximations). . Approximate a solution of :23 + sina: = 1 within 10’4 using Newton’s method. The A+ Question Use mathematical induction to prove that
n(n + 1)] 9—1 2 ...
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