Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 23, Problem 47RE
To determine
The derivative of the function
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7. Show that
An
→ A as n→∞
I{An} -
→ I{A} as n→ ∞.
7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A =
Un An, then P(A) is an increasing sequence converging to P(A).
(b) Repeat the same for a decreasing sequence.
(c) Show that the following inequalities hold:
P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A).
(d) Using the above inequalities, show that if A, A, then P(A) + P(A).
19. (a) Define the joint distribution and joint distribution function of a bivariate ran-
dom variable.
(b) Define its marginal distributions and marginal distribution functions.
(c) Explain how to compute the marginal distribution functions from the joint
distribution function.
Chapter 23 Solutions
Basic Technical Mathematics with Calculus (11th Edition)
Ch. 23.1 - Determine the continuity of the function
.
Ch. 23.1 - Prob. 2PECh. 23.1 -
Find .
Ch. 23.1 -
Find .
Ch. 23.1 - Prob. 1ECh. 23.1 - Prob. 2ECh. 23.1 - Prob. 3ECh. 23.1 - Prob. 4ECh. 23.1 - Prob. 5ECh. 23.1 - Prob. 6E
Ch. 23.1 - Prob. 7ECh. 23.1 - Prob. 8ECh. 23.1 - Prob. 9ECh. 23.1 - Prob. 10ECh. 23.1 - Prob. 11ECh. 23.1 - Prob. 12ECh. 23.1 - Prob. 13ECh. 23.1 - Prob. 14ECh. 23.1 - Prob. 15ECh. 23.1 - Prob. 16ECh. 23.1 - Prob. 17ECh. 23.1 - Prob. 18ECh. 23.1 - Prob. 19ECh. 23.1 - Prob. 20ECh. 23.1 - In Exercises 21–24, graph the function and...Ch. 23.1 - Prob. 22ECh. 23.1 - Prob. 23ECh. 23.1 - Prob. 24ECh. 23.1 - Prob. 25ECh. 23.1 - Prob. 26ECh. 23.1 - Prob. 27ECh. 23.1 - Prob. 28ECh. 23.1 - Prob. 29ECh. 23.1 - Prob. 30ECh. 23.1 - Prob. 31ECh. 23.1 - Prob. 32ECh. 23.1 - Prob. 33ECh. 23.1 - Prob. 34ECh. 23.1 - Prob. 35ECh. 23.1 - Prob. 36ECh. 23.1 - Prob. 37ECh. 23.1 - Prob. 38ECh. 23.1 - Prob. 39ECh. 23.1 - Prob. 40ECh. 23.1 - Prob. 41ECh. 23.1 - Prob. 42ECh. 23.1 - Prob. 43ECh. 23.1 - Prob. 44ECh. 23.1 - Prob. 45ECh. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - Prob. 48ECh. 23.1 - Prob. 49ECh. 23.1 - Prob. 50ECh. 23.1 - Prob. 51ECh. 23.1 - Prob. 52ECh. 23.1 - Prob. 53ECh. 23.1 - Prob. 54ECh. 23.1 - Prob. 55ECh. 23.1 - Prob. 56ECh. 23.1 - Prob. 57ECh. 23.1 - Prob. 58ECh. 23.1 - Prob. 59ECh. 23.1 - A 5-Ω resistor and a variable resistor of...Ch. 23.1 - Prob. 61ECh. 23.1 - Prob. 62ECh. 23.1 - Prob. 63ECh. 23.1 - Prob. 64ECh. 23.1 - Prob. 65ECh. 23.1 - Prob. 66ECh. 23.1 - Prob. 67ECh. 23.1 - Prob. 68ECh. 23.1 - Prob. 69ECh. 23.1 - Prob. 70ECh. 23.1 - Prob. 71ECh. 23.1 - Prob. 72ECh. 23.2 - Find the slope of a line tangent to the curve of y...Ch. 23.2 - Prob. 2PECh. 23.2 - Prob. 1ECh. 23.2 - Prob. 2ECh. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - Prob. 5ECh. 23.2 - Prob. 6ECh. 23.2 - In Exercises 7–10, use the method of Example 2 to...Ch. 23.2 - Prob. 8ECh. 23.2 - Prob. 9ECh. 23.2 - Prob. 10ECh. 23.2 - Prob. 11ECh. 23.2 - Prob. 12ECh. 23.2 - Prob. 13ECh. 23.2 - Prob. 14ECh. 23.2 - Prob. 15ECh. 23.2 - Prob. 16ECh. 23.2 - Prob. 17ECh. 23.2 - Prob. 18ECh. 23.2 - Prob. 19ECh. 23.2 - Prob. 20ECh. 23.2 - Prob. 21ECh. 23.2 - Prob. 22ECh. 23.2 - Prob. 23ECh. 23.2 - Prob. 24ECh. 23.2 - Prob. 25ECh. 23.2 - Prob. 26ECh. 23.2 - In Exercises 27–30, find the point(s) where the...Ch. 23.2 - Prob. 28ECh. 23.2 - Prob. 29ECh. 23.2 - Prob. 30ECh. 23.2 - Prob. 31ECh. 23.2 - Prob. 32ECh. 23.2 - Prob. 33ECh. 23.2 - Prob. 34ECh. 23.3 - Using the definiton, find the derivative of y = 5x...Ch. 23.3 - Prob. 2PECh. 23.3 - Prob. 1ECh. 23.3 - Prob. 2ECh. 23.3 - Prob. 3ECh. 23.3 - Prob. 4ECh. 23.3 - Prob. 5ECh. 23.3 - Prob. 6ECh. 23.3 - Prob. 7ECh. 23.3 - Prob. 8ECh. 23.3 - Prob. 9ECh. 23.3 - Prob. 10ECh. 23.3 - Prob. 11ECh. 23.3 - Prob. 12ECh. 23.3 - Prob. 13ECh. 23.3 - Prob. 14ECh. 23.3 - Prob. 15ECh. 23.3 - Prob. 16ECh. 23.3 - Prob. 17ECh. 23.3 - Prob. 18ECh. 23.3 - Prob. 19ECh. 23.3 - Prob. 20ECh. 23.3 - Prob. 21ECh. 23.3 - Prob. 22ECh. 23.3 - Prob. 23ECh. 23.3 - Prob. 24ECh. 23.3 - In Exercises 25–28, find the derivative of each...Ch. 23.3 - Prob. 26ECh. 23.3 - Prob. 27ECh. 23.3 - Prob. 28ECh. 23.3 - Prob. 29ECh. 23.3 - Prob. 30ECh. 23.3 - Prob. 31ECh. 23.3 - Prob. 32ECh. 23.3 - Prob. 33ECh. 23.3 - Prob. 34ECh. 23.3 - Prob. 35ECh. 23.3 - Prob. 36ECh. 23.3 - Prob. 37ECh. 23.3 - Prob. 38ECh. 23.3 - Prob. 39ECh. 23.3 - Prob. 40ECh. 23.4 - Prob. 1PECh. 23.4 - Prob. 2PECh. 23.4 - Prob. 1ECh. 23.4 - Prob. 2ECh. 23.4 - Prob. 3ECh. 23.4 - Prob. 4ECh. 23.4 - Prob. 5ECh. 23.4 - Prob. 6ECh. 23.4 - Prob. 7ECh. 23.4 - Prob. 8ECh. 23.4 - Prob. 9ECh. 23.4 - Prob. 10ECh. 23.4 - Prob. 11ECh. 23.4 - Prob. 12ECh. 23.4 - Prob. 13ECh. 23.4 - Prob. 14ECh. 23.4 - Prob. 15ECh. 23.4 - Prob. 16ECh. 23.4 - Prob. 17ECh. 23.4 - Prob. 18ECh. 23.4 - Prob. 19ECh. 23.4 - Prob. 20ECh. 23.4 - Prob. 21ECh. 23.4 - Prob. 22ECh. 23.4 - Prob. 23ECh. 23.4 - Prob. 24ECh. 23.4 - Prob. 25ECh. 23.4 - Prob. 26ECh. 23.4 - Prob. 27ECh. 23.4 - Prob. 28ECh. 23.4 - Prob. 29ECh. 23.4 - Prob. 30ECh. 23.4 - Prob. 31ECh. 23.4 - Prob. 32ECh. 23.4 - Prob. 33ECh. 23.4 - Prob. 34ECh. 23.4 - Prob. 35ECh. 23.4 - Prob. 36ECh. 23.4 - Prob. 37ECh. 23.4 - Prob. 38ECh. 23.4 - Prob. 39ECh. 23.4 - Prob. 40ECh. 23.4 - Prob. 41ECh. 23.4 - Prob. 42ECh. 23.4 - In Exercises 27–46, find the indicated...Ch. 23.4 - Prob. 44ECh. 23.4 - Prob. 45ECh. 23.4 - Prob. 46ECh. 23.5 - Prob. 1PECh. 23.5 - Prob. 2PECh. 23.5 - Prob. 1ECh. 23.5 - Prob. 2ECh. 23.5 - Prob. 3ECh. 23.5 - Prob. 4ECh. 23.5 - Prob. 5ECh. 23.5 - Prob. 6ECh. 23.5 - Prob. 7ECh. 23.5 - Prob. 8ECh. 23.5 - Prob. 9ECh. 23.5 - Prob. 10ECh. 23.5 - Prob. 11ECh. 23.5 - In Exercises 5–20, find the derivative of each of...Ch. 23.5 - Prob. 13ECh. 23.5 - Prob. 14ECh. 23.5 - Prob. 15ECh. 23.5 - Prob. 16ECh. 23.5 - Prob. 17ECh. 23.5 - Prob. 18ECh. 23.5 - Prob. 19ECh. 23.5 - Prob. 20ECh. 23.5 - Prob. 21ECh. 23.5 - Prob. 22ECh. 23.5 - Prob. 23ECh. 23.5 - Prob. 24ECh. 23.5 - Prob. 25ECh. 23.5 - Prob. 26ECh. 23.5 - Prob. 27ECh. 23.5 - Prob. 28ECh. 23.5 - Prob. 29ECh. 23.5 - Prob. 30ECh. 23.5 - Prob. 31ECh. 23.5 - Prob. 32ECh. 23.5 - Prob. 33ECh. 23.5 - Prob. 34ECh. 23.5 - Prob. 35ECh. 23.5 - Prob. 36ECh. 23.5 - Prob. 37ECh. 23.5 - Prob. 38ECh. 23.5 - Prob. 39ECh. 23.5 - Prob. 40ECh. 23.5 - Prob. 41ECh. 23.5 - Prob. 42ECh. 23.5 - Prob. 43ECh. 23.5 - Prob. 44ECh. 23.5 - Prob. 45ECh. 23.5 - Prob. 46ECh. 23.5 - Prob. 47ECh. 23.5 - Prob. 48ECh. 23.5 - Prob. 49ECh. 23.5 - Prob. 50ECh. 23.5 - Prob. 51ECh. 23.5 - Prob. 52ECh. 23.5 - Prob. 53ECh. 23.5 - Prob. 54ECh. 23.5 - Prob. 55ECh. 23.5 - Prob. 56ECh. 23.6 - Find the derivative of . Do not multiply factors...Ch. 23.6 - Prob. 2PECh. 23.6 - Prob. 1ECh. 23.6 - Prob. 2ECh. 23.6 - Prob. 3ECh. 23.6 - Prob. 4ECh. 23.6 - Prob. 5ECh. 23.6 - Prob. 6ECh. 23.6 - Prob. 7ECh. 23.6 - Prob. 8ECh. 23.6 - Prob. 9ECh. 23.6 - Prob. 10ECh. 23.6 - Prob. 11ECh. 23.6 - Prob. 12ECh. 23.6 - Prob. 13ECh. 23.6 - Prob. 14ECh. 23.6 - Prob. 15ECh. 23.6 - Prob. 16ECh. 23.6 - Prob. 17ECh. 23.6 - Prob. 18ECh. 23.6 - Prob. 19ECh. 23.6 - Prob. 20ECh. 23.6 - Prob. 21ECh. 23.6 - Prob. 22ECh. 23.6 - Prob. 23ECh. 23.6 - Prob. 24ECh. 23.6 - Prob. 25ECh. 23.6 - Prob. 26ECh. 23.6 - Prob. 27ECh. 23.6 - Prob. 28ECh. 23.6 - Prob. 29ECh. 23.6 - Prob. 30ECh. 23.6 - Prob. 31ECh. 23.6 - Prob. 32ECh. 23.6 - Prob. 33ECh. 23.6 - Prob. 34ECh. 23.6 - Prob. 35ECh. 23.6 - Prob. 36ECh. 23.6 - Prob. 37ECh. 23.6 - Prob. 38ECh. 23.6 - Prob. 39ECh. 23.6 - Prob. 40ECh. 23.6 - Prob. 41ECh. 23.6 - Prob. 42ECh. 23.6 - Prob. 43ECh. 23.6 - Prob. 44ECh. 23.6 - In Exercises 33–58, solve the given problems by...Ch. 23.6 - Prob. 46ECh. 23.6 - Prob. 47ECh. 23.6 - Prob. 48ECh. 23.6 - Prob. 49ECh. 23.6 - Prob. 50ECh. 23.6 - Prob. 51ECh. 23.6 - Prob. 52ECh. 23.6 - Prob. 53ECh. 23.6 - Prob. 54ECh. 23.6 - Prob. 55ECh. 23.6 - Prob. 56ECh. 23.6 - Prob. 57ECh. 23.6 - Prob. 58ECh. 23.7 - Prob. 1PECh. 23.7 - Prob. 2PECh. 23.7 - Prob. 3PECh. 23.7 - Prob. 4PECh. 23.7 - Prob. 1ECh. 23.7 - Prob. 2ECh. 23.7 - Prob. 3ECh. 23.7 - Prob. 4ECh. 23.7 - Prob. 5ECh. 23.7 - Prob. 6ECh. 23.7 - Prob. 7ECh. 23.7 - Prob. 8ECh. 23.7 - Prob. 9ECh. 23.7 - Prob. 10ECh. 23.7 - Prob. 11ECh. 23.7 - Prob. 12ECh. 23.7 - Prob. 13ECh. 23.7 - Prob. 14ECh. 23.7 - Prob. 15ECh. 23.7 - Prob. 16ECh. 23.7 - Prob. 17ECh. 23.7 - Prob. 18ECh. 23.7 - Prob. 19ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 21ECh. 23.7 - Prob. 22ECh. 23.7 - Prob. 23ECh. 23.7 - Prob. 24ECh. 23.7 - Prob. 25ECh. 23.7 - Prob. 26ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 28ECh. 23.7 - Prob. 29ECh. 23.7 - Prob. 30ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 32ECh. 23.7 - Prob. 33ECh. 23.7 - Prob. 34ECh. 23.7 - Prob. 35ECh. 23.7 - Prob. 36ECh. 23.7 - Prob. 37ECh. 23.7 - Prob. 38ECh. 23.7 - Prob. 39ECh. 23.7 - Prob. 40ECh. 23.7 - Prob. 41ECh. 23.7 - Prob. 42ECh. 23.7 - Prob. 43ECh. 23.7 - Prob. 44ECh. 23.7 - Prob. 45ECh. 23.7 - Prob. 46ECh. 23.7 - Prob. 47ECh. 23.7 - Prob. 48ECh. 23.7 - Prob. 49ECh. 23.7 - Prob. 50ECh. 23.7 - Prob. 51ECh. 23.7 - Prob. 52ECh. 23.7 - Prob. 53ECh. 23.7 - Prob. 54ECh. 23.7 - Prob. 55ECh. 23.7 - Prob. 56ECh. 23.7 - Prob. 57ECh. 23.7 - Prob. 58ECh. 23.8 - Prob. 1PECh. 23.8 - Prob. 1ECh. 23.8 - Prob. 2ECh. 23.8 - In Exercises 3–22, find dy/dx by differentiating...Ch. 23.8 - Prob. 4ECh. 23.8 - Prob. 5ECh. 23.8 - Prob. 6ECh. 23.8 - Prob. 7ECh. 23.8 - Prob. 8ECh. 23.8 - Prob. 9ECh. 23.8 - Prob. 10ECh. 23.8 - Prob. 11ECh. 23.8 - Prob. 12ECh. 23.8 - Prob. 13ECh. 23.8 - Prob. 14ECh. 23.8 - Prob. 15ECh. 23.8 - Prob. 16ECh. 23.8 - Prob. 17ECh. 23.8 - Prob. 18ECh. 23.8 - Prob. 19ECh. 23.8 - Prob. 20ECh. 23.8 - Prob. 21ECh. 23.8 - Prob. 22ECh. 23.8 - Prob. 23ECh. 23.8 - Prob. 24ECh. 23.8 - Prob. 25ECh. 23.8 - Prob. 26ECh. 23.8 - Prob. 27ECh. 23.8 - Prob. 28ECh. 23.8 - Prob. 29ECh. 23.8 - Prob. 30ECh. 23.8 - Prob. 31ECh. 23.8 - Prob. 32ECh. 23.8 - Prob. 33ECh. 23.8 - Prob. 34ECh. 23.8 - Prob. 35ECh. 23.8 - Prob. 36ECh. 23.8 - Prob. 37ECh. 23.8 - Prob. 38ECh. 23.8 - Prob. 39ECh. 23.8 - Prob. 40ECh. 23.8 - Prob. 41ECh. 23.8 - Prob. 42ECh. 23.8 - Prob. 43ECh. 23.8 - Prob. 44ECh. 23.9 - Prob. 1PECh. 23.9 - Prob. 2PECh. 23.9 - Prob. 1ECh. 23.9 - Prob. 2ECh. 23.9 - Prob. 3ECh. 23.9 - Prob. 4ECh. 23.9 - Prob. 5ECh. 23.9 - Prob. 6ECh. 23.9 - Prob. 7ECh. 23.9 - Prob. 8ECh. 23.9 - Prob. 9ECh. 23.9 - Prob. 10ECh. 23.9 - Prob. 11ECh. 23.9 - Prob. 12ECh. 23.9 - Prob. 13ECh. 23.9 - Prob. 14ECh. 23.9 - Prob. 15ECh. 23.9 - Prob. 16ECh. 23.9 - Prob. 17ECh. 23.9 - Prob. 18ECh. 23.9 - Prob. 19ECh. 23.9 - Prob. 20ECh. 23.9 - Prob. 21ECh. 23.9 - Prob. 22ECh. 23.9 - Prob. 23ECh. 23.9 - Prob. 24ECh. 23.9 - Prob. 25ECh. 23.9 - Prob. 26ECh. 23.9 - Prob. 27ECh. 23.9 - Prob. 28ECh. 23.9 - Prob. 29ECh. 23.9 - Prob. 30ECh. 23.9 - Prob. 31ECh. 23.9 - Prob. 32ECh. 23.9 - Prob. 33ECh. 23.9 - Prob. 34ECh. 23.9 - Prob. 35ECh. 23.9 - Prob. 36ECh. 23.9 - Prob. 37ECh. 23.9 - Prob. 38ECh. 23.9 - Prob. 39ECh. 23.9 - Prob. 40ECh. 23.9 - Prob. 41ECh. 23.9 - Prob. 42ECh. 23.9 - Prob. 43ECh. 23.9 - Prob. 44ECh. 23.9 - Prob. 45ECh. 23.9 - Prob. 46ECh. 23.9 - Prob. 47ECh. 23.9 - Prob. 48ECh. 23.9 - Prob. 49ECh. 23.9 - Prob. 50ECh. 23.9 - Prob. 51ECh. 23.9 - Prob. 52ECh. 23 - Prob. 1RECh. 23 - Prob. 2RECh. 23 - Prob. 3RECh. 23 - Prob. 4RECh. 23 - Prob. 5RECh. 23 - Prob. 6RECh. 23 - Prob. 7RECh. 23 - Prob. 8RECh. 23 - Prob. 9RECh. 23 - Prob. 10RECh. 23 - Prob. 11RECh. 23 - Prob. 12RECh. 23 - Prob. 13RECh. 23 - Prob. 14RECh. 23 - Prob. 15RECh. 23 - Prob. 16RECh. 23 - Prob. 17RECh. 23 - Prob. 18RECh. 23 - Prob. 19RECh. 23 - Prob. 20RECh. 23 - In Exercises 21–28, use the definition to find the...Ch. 23 - Prob. 22RECh. 23 - Prob. 23RECh. 23 - Prob. 24RECh. 23 - Prob. 25RECh. 23 - Prob. 26RECh. 23 - Prob. 27RECh. 23 - Prob. 28RECh. 23 - Prob. 29RECh. 23 - Prob. 30RECh. 23 - Prob. 31RECh. 23 - Prob. 32RECh. 23 - Prob. 33RECh. 23 - Prob. 34RECh. 23 - Prob. 35RECh. 23 - Prob. 36RECh. 23 - Prob. 37RECh. 23 - Prob. 38RECh. 23 - Prob. 39RECh. 23 - Prob. 40RECh. 23 - Prob. 41RECh. 23 - Prob. 42RECh. 23 - Prob. 43RECh. 23 - Prob. 44RECh. 23 - Prob. 45RECh. 23 - Prob. 46RECh. 23 - Prob. 47RECh. 23 - Prob. 48RECh. 23 - Prob. 49RECh. 23 - Prob. 50RECh. 23 - Prob. 51RECh. 23 - Prob. 52RECh. 23 - Prob. 53RECh. 23 - Prob. 54RECh. 23 - Prob. 55RECh. 23 - Prob. 56RECh. 23 - Prob. 57RECh. 23 - Prob. 58RECh. 23 - Prob. 59RECh. 23 - Prob. 60RECh. 23 - Prob. 61RECh. 23 - Prob. 62RECh. 23 - Prob. 63RECh. 23 - Prob. 64RECh. 23 - If $5000 is invested at interest rate i,...Ch. 23 - The temperature T (in °C) of a rotating machine...Ch. 23 - Prob. 67RECh. 23 - Prob. 68RECh. 23 - Prob. 69RECh. 23 - Prob. 70RECh. 23 - Prob. 71RECh. 23 - Prob. 72RECh. 23 - Prob. 73RECh. 23 - Prob. 74RECh. 23 - Prob. 75RECh. 23 - Prob. 76RECh. 23 - Prob. 77RECh. 23 - Prob. 78RECh. 23 - Prob. 79RECh. 23 - Prob. 80RECh. 23 - Prob. 81RECh. 23 - Prob. 82RECh. 23 - Prob. 83RECh. 23 - Prob. 84RECh. 23 - Prob. 85RECh. 23 - Prob. 86RECh. 23 - Prob. 87RECh. 23 - Prob. 88RECh. 23 - Prob. 89RECh. 23 - Prob. 90RECh. 23 - Prob. 91RECh. 23 - Prob. 92RECh. 23 - Prob. 93RECh. 23 - Prob. 94RECh. 23 - Prob. 95RECh. 23 - Prob. 96RECh. 23 - Prob. 97RECh. 23 - Prob. 98RECh. 23 - In Exercises 53–98, solve the given problems.
99....Ch. 23 - Prob. 1PTCh. 23 - Prob. 2PTCh. 23 - Prob. 3PTCh. 23 - Prob. 4PTCh. 23 - Prob. 5PTCh. 23 - Prob. 6PTCh. 23 - Prob. 7PTCh. 23 - Prob. 8PTCh. 23 - Prob. 9PTCh. 23 - Prob. 10PT
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