- Solutions -2.1/2.2 Limit Laws (1) Show that for all numbers a, c, d,
- Solutions -4.1 -continued (8) In class we prove Theorem 4.7 (Power Rule) for positive integers. Use that result, along
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- Solutions -3.2 (2) Find inf S and sup S, and state whether or not these are contained in S.
- Solutions -3.7 (13) (a) Show that the family F of all intervals of the form In = ( 1
- Solutions -9.3 (1) Show that the sequence {fn} converges to f for each x in I. Determine whether or not
- Solutions -9.1 continued (5) Show whether the following series converges or diverges.
- Solutions -9.2 continued (1) Show whether the following series is absolutely convergent, conditionally convergent or
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- Solutions -3.5 (5) Show that the function f(x) = 1
- Solutions -3.6 (4) Decide if the given sequence is a Cauchy sequence. If it is, prove it. If it is not, a
- Solutions -3.7 Cantor Set (A) Use the geometric series formula (from Calc 2) to show that
- Solutions -6.1 (1) Show that Rn
- Problems -2.5 -Limits of Sequences (1) Given the function f(x) = x cos x.
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- 1.15 Homework Solutions -Limits (1a) Show lim
- Solutions -Sections 50, 51, 52 (1a) f(z) = e-z
- 1.11 -Solutions (11.A) Show |z| > 2 is open using the formal neighborhood definition.
- Solutions -Section 43 (4) CR is the upper half circle |z| = R, counterclockwise. Assume R > 2.
- 1.1 -1.4 Homework Solutions (2.2b) Prove that Im(iz) = Re z.
- Solutions -Sections 30 and 31 3) = ln 2 + i(
- Solutions -Section 26 (1) Show that u is harmonic and find a harmonic conjugate.
- 1.5 -1.8 Homework Problems (5.1) Use properties of conjugates and moduli to show the equality
- Section 23 Solutions (8) We know that if f is differentiable at z0 then
- Section 20 Solutions (20.8a) Show that f(z) = Re z is not differentiable for any z by showing the limit in the
- 1.5 -1.8 Homework Problems (5.1) Use properties of conjugates and moduli to show the equality
- Math 322 Midterm 1 Practice Midterm 1 will cover sections 1.1-1.8 and 2.1-2.3. You can bring one sheet of notes (front
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