CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
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Textbook Question
Chapter H, Problem 25E
Write the number in polar form with argument between 0 and 2π.
25. −3 + 3i
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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
Chapter H Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
Ch. H - Prob. 1ECh. H - Prob. 2ECh. H - Prob. 3ECh. H - Prob. 4ECh. H - Prob. 5ECh. H - Prob. 6ECh. H - Prob. 7ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 9ECh. H - Prob. 10E
Ch. H - Prob. 11ECh. H - Prob. 12ECh. H - Prob. 13ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 15ECh. H - Prob. 16ECh. H - Prob. 17ECh. H - Prove the following properties of complex numbers....Ch. H - Prob. 19ECh. H - Prob. 20ECh. H - Prob. 21ECh. H - Find all solutions of the equation. 22. 2x2 2x +...Ch. H - Prob. 23ECh. H - Find all solutions of the equation. 24....Ch. H - Write the number in polar form with argument...Ch. H - Prob. 26ECh. H - Prob. 27ECh. H - Prob. 28ECh. H - Write the number in polar form with argument...Ch. H - Prob. 30ECh. H - Prob. 31ECh. H - Prob. 32ECh. H - Find the indicated power using De Moivres Theorem....Ch. H - Prob. 34ECh. H - Prob. 35ECh. H - Prob. 36ECh. H - Prob. 37ECh. H - Prob. 38ECh. H - Prob. 39ECh. H - Prob. 40ECh. H - Prob. 41ECh. H - Prob. 42ECh. H - Prob. 43ECh. H - Prob. 44ECh. H - Prob. 45ECh. H - Prob. 46ECh. H - Prob. 47ECh. H - Use Eulers formula to prove the following formulas...Ch. H - If u(x) = f(x) + ig(x) is a complex-valued...Ch. H - (a) If u is a complex-valued function of a real...
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