The number e i π 2 in the form a + b i .

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Chapter H, Problem 41E

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To write: The number eiπ2 in the form a+bi.

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3. (i) Let A, B, C, D, E be positive constants. Find the limit n³ D lim A(BC)³ +1 en 4+E. n→∞ [6 Marks] (ii) Let X be a random variable with the standard normal distribution, i.e. X has the probability density function Let 1 f(x) √2π n3x2 Xn = 100(50 +X6) en³4, n = 1, 2,..., 3+1 (a) Find the limit lim∞ Xn, verify your answer. Y = 100(50 +X) 22. [6 Marks] (b) Is Xn≤Y? Verify your answer. [6 Marks] (c) Is EY∞o? Verify your answer. [6 Marks] (d) Does lim∞ EXn (e) Find lim∞ EXn. Elim Xn? Why? [6 Marks] [3 Marks]

3. (i) Using the definition of the line integral of a vector field, calculate the line integral L³ F.dy of the vector field F: R² → R² given by F(x, y) = (y, x), and where the curve & is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]

1. Evaluate the integral ↓ f(x, y)dxdy, of function f R² →R over the domain DC R2, where: f(x, y) = 2x + y and D is the is the triangle with vertices (0, -1), (1,0) and (0,2). Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for some a

Answer 2

Question

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

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Answer 3

Question

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

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Answer 4

Question

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

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Answer 5

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

Answer 6

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

Answer 7

Chapter H, Problem 41E

To determine

To write: The number eiπ2 in the form a+bi.

Answer 8

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Answer 9

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Answer 11

Ch. H - Prob. 1E Ch. H - Prob. 2E Ch. H - Prob. 3E Ch. H - Prob. 4E Ch. H - Prob. 5E Ch. H - Prob. 6E Ch. H - Prob. 7E Ch. H - Evaluate the expression and write your answer in...Ch. H - Prob. 9E Ch. H - Prob. 10E

The number e i π 2 in the form a + b i .

Solution Summary: The author explains how to simplify the number eipi by using Euler's formula.

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To write: The number eiπ2 in the form a+bi.

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Chapter H Solutions