Calculus with Applications (11th Edition)
11th Edition
ISBN: 9780321979421
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 4, Problem 66RE
To determine
To explain: Why e is a convenient base for exponential and logarithmic functions.
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3
Evaluate the double integral 10
y√x dy dx. First sketch the area of the integral involved, then
carry out the integral in both ways, first over x and next over y, and vice versa.
Question 2.
i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) =
P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y
have the same distribution? Explain your answer.
ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random
variable? Do X and Y have the same distribution? Explain your answer.
Problem 4. Let
f(x, y) =
{
Find P(X <1/2|Y = 1/2).
c(x + y²) 0
Chapter 4 Solutions
Calculus with Applications (11th Edition)
Ch. 4.1 - YOUR TURN 1 find f′(t).
Ch. 4.1 - YOUR TURN 2 find dy/dx.
Ch. 4.1 - Prob. 3YTCh. 4.1 - Prob. 4YTCh. 4.1 - Prob. 5YTCh. 4.1 - Prob. 1WECh. 4.1 - Prob. 2WECh. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...
Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Prob. 21ECh. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - 23. Which of the following describes the...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Find each derivative.
27.
Ch. 4.1 - Find each derivative.
28.
Ch. 4.1 - Prob. 29ECh. 4.1 - Find each derivative.
30.f′(3) if
Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - 44. If g′(5) = 12 and h′ (5) = −3, find f′ (5) for...Ch. 4.1 - Prob. 45ECh. 4.1 - 46. Use the information given in the figure to...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - 65. Track and Field In 1906 Kennelly developed a...Ch. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Velocity We saw in the previous chapter that if a...Ch. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - 73. Velocity A ball is thrown vertically upward...Ch. 4.1 - 74. Dead Sea Researchers who have been studying...Ch. 4.1 - Prob. 75ECh. 4.1 - 76. AP Examination The probability (as a percent)...Ch. 4.1 - 77. Dog’s Human Age From the data printed in the...Ch. 4.2 - YOUR TURN 1 Find the derivative of y = (x3 + 7)(4...Ch. 4.2 - YOUR TURN 2 Find f′(x) if
Ch. 4.2 - Prob. 3YTCh. 4.2 - Prob. 4YTCh. 4.2 - Prob. 1WECh. 4.2 - Prob. 2WECh. 4.2 - Prob. 3WECh. 4.2 - Prob. 1ECh. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 29ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - 34. Find an equation of the line tangent to the...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - 38. Use the fact that f(x) = u(x)/v(x) can be...Ch. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - 48. Revenue Suppose that at the beginning of the...Ch. 4.2 - Prob. 49ECh. 4.2 - 50. Muscle Reaction When a certain drug is...Ch. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - 54. Memory Retention Some psychologists contend...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.3 - YOUR TURN 1 For the functionsin Example 1, find...Ch. 4.3 - Prob. 2YTCh. 4.3 - Prob. 3YTCh. 4.3 - Prob. 4YTCh. 4.3 - Prob. 5YTCh. 4.3 - Prob. 6YTCh. 4.3 - Prob. 7YTCh. 4.3 - Prob. 1WECh. 4.3 - Prob. 2WECh. 4.3 - Prob. 3WECh. 4.3 - Prob. 1ECh. 4.3 - Let f(x) = 5x2 − 2x and g(x) = 8x + 3.
2....Ch. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Find f[g(x)] and g[f(x)].
8. f(x) = −8x + 9;
Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Find f[g(x)] and g[f(x)].
12. f(x) = 8x2 − 11x;
Ch. 4.3 - Find f[g(x)] and g[f(x)].
13. ;
Ch. 4.3 - Find f[g(x)] and g[f(x)].
14. ;
Ch. 4.3 - Prob. 15ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 17ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 19ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 21ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - 52. Mrugy and Nate are working on taking the...Ch. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - 56. Demand Suppose a demand function is given...Ch. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - 63. To test an individual’s use of calcium, a...Ch. 4.3 - Prob. 64ECh. 4.4 - YOUR TURN 1 Find dy/dx for
y = 43x,
y = e3x+5.
Ch. 4.4 - Prob. 2YTCh. 4.4 - Prob. 3YTCh. 4.4 - Prob. 4YTCh. 4.4 - Prob. 1WECh. 4.4 - Prob. 2WECh. 4.4 - Prob. 3WECh. 4.4 - Prob. 1ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 21ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 32ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - 40. Sales The sales of a new personal computer (in...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - 44. Investment The value of a particular...Ch. 4.4 - Prob. 45ECh. 4.4 - 46. Population Growth In Section 10.4, Exercise...Ch. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - 63. The Gateway Arch The Gateway Arch in St....Ch. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.5 - YOUR TURN 1 Find the derivative of f(x) = log3x.
Ch. 4.5 - Prob. 2YTCh. 4.5 - Prob. 3YTCh. 4.5 - Prob. 1WECh. 4.5 - Prob. 2WECh. 4.5 - Prob. 3WECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Find the derivative of each function.
4. y = ln(1...Ch. 4.5 - Prob. 5ECh. 4.5 - Find the derivative of each function.
6. y =...Ch. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Find the derivative of each function.
9.
Ch. 4.5 - Prob. 10ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 40ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Use the ideas from Exercise 53 to find the...Ch. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - 57. Revenue Suppose the demand function for q...Ch. 4.5 - 58. Profit If the cost function in dollars for q...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - 67. Richter Scale Richter Scale The Richter scale...Ch. 4.5 - Prob. 68ECh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Find the slope of the tangent line to the given...Ch. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 93RE
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