MATHEMATICS 120 PROBLEM SET 1
Instead of the first homework, there will be a quiz on Wednesday, September 11, in class.
The practice problems below will help you prepare for the quiz. They are review problems,
meant to test your general mathematical background, and do not require any knowledge of
calculus. Solutions will be presented in class on Tuesday, September 10. Do not hand in
your answers, as they will not be marked. You should, however, write up your solutions
so that you can check them against those given in Tuesday’s class.
1. (a) Sketch the graphs of the functions f (x) = sin( x1 ) and g(x) = x12 sin( x1 ). Are f and
g even, odd, or neither? Indicate what happens when x is close to 0.
(b) If g(x) is as in (a), find three different values of x such that |x| ≤ 0.001 and g(x) = 0.
Also find three different values of x such that |x| ≤ 0.001 and g(x) ≥ 1000.
2. Find the equation of the circle centered at the point (−1, 3) and tangent to the line
y = 12 x − 4.
3. Let f (x) be a function such that the graph of f (x) is symmetric about the line x = 1,
and also symmetric about the line x = 5. Prove that f (x + 8) = f (x) for all x (i.e. f (x)
is periodic with period 8).
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