Reference no: EM131077493
Sample midterm 1 questions-
1. By using appropriate series tests, determine whether
n=0Σ∞(1/4n + (1/2)n, n=1Σ∞sin nπ/4, n=1Σ∞(1/n log n)
converge or diverge.
2. (a) Calculate the exact interval of convergence of
n=0Σ∞ yn/3n.
(b) Sketch the function f(x) = 3 + (x2 - 1)(x2 - 4) over the range -3 < x < 3.
(c) Determine the exact ranges of convergence of
n=0Σ∞ f(x)n/3n.
3. Consider a right-angled triangle with vertices at (0, 0), (0, 1), and (1, 0), with non-uniform density ρ(x, y) = y. Find its center of mass.
4. Find the minimum and maximum values of the function f(x, y) = (x - 2y)2 - x in the square |x| ≤ 1, |y| ≤ 1.
5. Consider an asymmetric tent design of length l that is comprised of a vertical section of height h, connected to a diagonal section, as shown in the diagram below.
The volume of the tent is hl2/2. For a fixed area of tent material A, find the values of h and l that maximise the tent's volume.
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