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Due date if any
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Fuchsia means graded homework.
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Section 9.1.2, page 439: 1, 2, 3a.
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We have the power series of sin(θ) and of cos(θ).
Give the first 5 terms of the power series of tan(θ) (some of the terms
will be equal to 0, very convenient!).
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Section 9.1.1, page 434: 5 (radians only).
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Section 8.3.2, page 426: 7.
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Section 8.3.1, page 418: 1.
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Section 8.2.5, page 407: 5b.
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Section 8.2.2, page 395: 1, 6.
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Section 8.1.4, page 382: 2, 10a.
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Section 8.1.3, page 378: 7.
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Section 8.1.2, page 374: 1, 5.
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See page 364: Draw an arbitrary line and point in the plane.
Explain where the points on the line are that are closest to the point, using
the taxicab distance (beware that there are special cases if line and point are
specially chosen).
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See page 355, figure 85: Draw two `arbitrary' rotation congruent triangles, and
show how to construct the location of the center of rotation.
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See page 352: Prove that the sum of opposite angles of a cyclic quadrilateral
equals 180 degrees, that is π.
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Section 7.4.1, page 350: 5 trace the line of reflection.
Section 7.3.2, page 343: 1, 2 describe all symmetries of the `infinite' checker
board, 6bc, 13ac.
Section 7.3.1, page 338: 1, 4, 10bc, 11.
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Give the 2 by 2 matrix which rotates the plane around the origin (0,0) by
30 degrees, that is π / 6, clockwise.
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Give the 2 by 2 matrix which rotates the plane around the origin (0,0) by
45 degrees, that is π / 4, clockwise.
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Give the 2 by 2 matrix which rotates the plane around the origin (0,0) by
45 degrees, that is π / 4, counter-clockwise.
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Give the 2 by 2 matrix which rotates the plane around the origin (0,0) by
90 degrees, that is π / 2, counter-clockwise.
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Rotate the circle with equation (x-3)^2 + y^2 = 1 by 90 degrees around point
(-5,0) counter-clockwise. What is its new equation?
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Section 7.2.1, page 304: 1, 3.
Section 7.1.4, page 302: 3, 4.
Section 7.1.3, page 294: 4, 5, 7, 8.
Section 7.1.2, page 289: 1, 5.
(A tromino is like a domino, but consists of 3 squares in a row instead of 2.
Can we cover an 8 by 8 chess board with trominoes, if not why not?)
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Section 3.3.3, page 129: 5, 6a.
Section 3.3.2, page 124: 1a, 4ab, write p(x) = x^3 in factorial form.
Section 3.3.1, page 121: 9.
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Simplify the sum of the binomial coefficients C^n_k + C^n_(k+1) as a single
binomial coefficient.
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Given function f(x) = x^2 - 1, find an inverse function with maximal domain
and codomain.
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Give the definition of a one-to-one relation R from A to B.
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Sections 3.3.X, how about a project on Δ f and D f, where (Δ f)(n)
= f(n+1) - f(n), and (D f)(n) = f(n+1), a version of `discrete' calculus?
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Section 3.2.4, page 112: 1de, 7.
Section 3.2.3, page 105: 3, 4, 7a, 12.
Section 3.2.2, page 100: 1, 2, 5, 6a, 7, 9a.
Section 3.2.1, page 94: 1abd, 3bc, 13a.
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19 March
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We are given numbers a and b.
We define the sequence s_0, s_1, s_2, s_3, and so on, by the equations
s_0 = 1 and
s_(n+1) = a * s_n + b for all n.
Find a general `nice' formula for s_n.
There may be special cases for very special values of a or b.
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Section 3.1.3, page 85: 2, 4, 7, 10a.
Section 3.1.2, page 79: 1 and 2 (with Alice a(t) = v_1 * t and Bob b(t) = v_2 *
(t - d) where v_1 and v_2 are their speeds, and d is the delay), 6.
Section 3.1.1, page 75: 2ac, 5, 6.
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Section 2.2.2, page 62: 1acd, 4 (write z = x + iy), 10a.
Section 2.2.1, page 53: 1bf, 3, 6bc.
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Section 2.1.4, page 46: 1a, 2a, 5cd, 8ab.
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Is (√ 2 + ∛ 5) an algebraic number?
If so, give an integer coefficient polynomial of which it is a root.
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Section 2.1.3, page 39: 3a, 5b, 8.
Section 2.1.2, page 33: 1.
Section 2.1.1, page 24: 1a, 2a, 3a (harder), 4a, 8, 9a, 12a.
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