Applied Calculus
7th Edition
ISBN: 9781337291248
Author: Waner, Stefan.
Publisher: Cengage Learning,
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Textbook Question
Chapter 4.1, Problem 56E
In Exercises 53–58, find the slope of the tangent to the graph of the given function at the indicated point. [HINT: Recall that the slope of the tangent to the graph of
is
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3.12 (B). A horizontal beam AB is 4 m
long and of constant flexural rigidity. It is
rigidly built-in at the left-hand end A and simply supported on a non-yielding support
at the right-hand end B. The beam carries Uniformly distributed vertical loading of
18 kN/m over its whole length, together with a vertical downward load of 10KN at
2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating
all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7
Qize
f(x)
=
x + 2x2 - 2
x² + 4x²² -
Solve the equation using Newton
Raphson
-b±√√b2-4ac
2a
@4x²-12x+9=0
27 de febrero de 2025
-b±√√b2-4ac
2a
⑥2x²-4x-1=0
a = 4 b=-12
c=9
a = 2
b = 9
c = \
x=-42±√(2-4 (4) (9)
2(4))
X =
(12) ±√44)-(360)
2(108)
x = ±√
X = =±√√²-4(2) (1)
2()
X = ±√
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X =
X =
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X₁ =
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X₁ =
X₁ =
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X₁ =
=
=
Chapter 4 Solutions
Applied Calculus
Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - Prob. 2ECh. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...Ch. 4.1 - In Exercises 1-10, use the shortcut rules to...
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 4.1 - Prob. 16ECh. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - In Exercises 17-40, find the derivative of the...Ch. 4.1 - Prob. 40ECh. 4.1 - In Exercises 41-46, evaluate the given expression....Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - In Exercises 41-46, evaluate the given expression....Ch. 4.1 - In Exercises 47-52, find the indicated derivative....Ch. 4.1 - In Exercises 47-52, find the indicated derivative....Ch. 4.1 - In Exercises 47-52, find the indicated derivative....Ch. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - In Exercises 5358, find the slope of the tangent...Ch. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - In Exercises 5358, find the slope of the tangent...Ch. 4.1 - In Exercises 5358, find the slope of the tangent...Ch. 4.1 - In Exercises 5358, find the slope of the tangent...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 5964, find the equation of the...Ch. 4.1 - In Exercises 6570, find all values of x (if any)...Ch. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - In Exercises 6570, find all values of x (if any)...Ch. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - If Exercises 73-76, determine whether f is...Ch. 4.1 - If Exercises 73-76, determine whether f is...Ch. 4.1 - If Exercises 73-76, determine whether f is...Ch. 4.1 - If Exercises 73-76, determine whether f is...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 4.1 - Crude Oil Prices The price per barrel of crude oil...Ch. 4.1 - Median Home Price The median home price in the...Ch. 4.1 - Food versus Education The following equation shows...Ch. 4.1 - Food versus Recreation The following equation...Ch. 4.1 - Velocity If a stone is dropped from a height of...Ch. 4.1 - Velocity If a stone is thrown down at 120 ft/sec...Ch. 4.1 - Velocity The height of a soccer ball kicked by...Ch. 4.1 - Velocity The height of a basketball thrown by...Ch. 4.1 - GE Net Income 2009-2013 The annual net income of...Ch. 4.1 - GE Net Income 20072011 The annual net income of...Ch. 4.1 - Ecology Increasing numbers of manatees (sea...Ch. 4.1 - SAT Scores by Income The following graph shown...Ch. 4.1 - Prob. 101ECh. 4.1 - Market Share: Smartphones The following graph...Ch. 4.1 - Prob. 103ECh. 4.1 - Prob. 104ECh. 4.1 - Prob. 105ECh. 4.1 - Prob. 106ECh. 4.1 - Prob. 107ECh. 4.1 - Prob. 108ECh. 4.1 - Following is an excerpt from your best friends...Ch. 4.1 - Following is an excerpt from your own graded...Ch. 4.1 - Following is an excerpt from your best friends...Ch. 4.1 - Following is an excerpt from your second best...Ch. 4.1 - Following is an excerpt from your second best...Ch. 4.1 - Following is an excerpt from your second enemys...Ch. 4.1 - Prob. 115ECh. 4.1 - Prob. 116ECh. 4.1 - Prob. 117ECh. 4.1 - Prob. 118ECh. 4.2 - In Exercises 14, for each cost function, find the...Ch. 4.2 - In Exercises 14, for each cost function, find the...Ch. 4.2 - In Exercises 14, for each cost function, find the...Ch. 4.2 - In Exercises 14, for each cost function, find the...Ch. 4.2 - In Exercises 5 and 6, find the marginal cost,...Ch. 4.2 - In Exercises 5 and 6, find the marginal cost,...Ch. 4.2 - A certain cost function has the following graph:...Ch. 4.2 - A certain cost function has the following graph:...Ch. 4.2 - Advertising Costs The cost, in thousands of...Ch. 4.2 - Prob. 10ECh. 4.2 - Marginal and Average Cost: iPhones Assume that it...Ch. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Marginal Revenue and Profit The Audubon Society at...Ch. 4.2 - Marginal Profit Suppose P(x) represents the profit...Ch. 4.2 - Marginal Loss An automobile retailer calculates...Ch. 4.2 - Marginal Profit Your monthly profit (in dollars)...Ch. 4.2 - Marginal Profit Your monthly profit (in dollars)...Ch. 4.2 - Marginal Revenue: Pricing Tuna Assume that the...Ch. 4.2 - Marginal Revenue: Pricing Tuna Repeat Exercise 19,...Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Fuel Economy Your Porsches gas mileage (in miles...Ch. 4.2 - Marginal Revenue The estimated marginal revenue...Ch. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - For the cost function C(x)=mx+b themarginal cost...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 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. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - In Exercises 13-28, calculate dydx. Simplify your...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - In Exercises 29-56, calculate dydx. You need not...Ch. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - In Exercises 57-62, compute the indicated...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - In Exercises 71-76, find the equation of the line...Ch. 4.3 - In Exercises 71-76, find the equation of the line...Ch. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Revenue The monthly sales of Sunny Electronics new...Ch. 4.3 - Revenue The monthly sales of Sunny Electronics new...Ch. 4.3 - Saudi Oil Revenues The price of crude oil during...Ch. 4.3 - Russian Oil Revenues The price of crude oil during...Ch. 4.3 - Revenue Dorothy Wagner is currently selling 20 I ...Ch. 4.3 - Pricing Policy Let us turn Exercise 81 around a...Ch. 4.3 - Bus Travel Thoroughbred Bus Company finds that its...Ch. 4.3 - Prob. 84ECh. 4.3 - Fuel Economy Your muscle cars gas mileage (in...Ch. 4.3 - Fuel Economy Your used Chevys gas mileage (in...Ch. 4.3 - Prob. 87ECh. 4.3 - Oil Imports from Mexico Daily oil production in...Ch. 4.3 - Prob. 89ECh. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Biology-Reproduction Another model, the predator...Ch. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - If f and g are functions of time, and at time t=3,...Ch. 4.3 - If f and g are functions of time, and at time t=2,...Ch. 4.3 - If f and g are functions of time, and at time t=3,...Ch. 4.3 - Prob. 98ECh. 4.3 - Prob. 99ECh. 4.3 - Prob. 100ECh. 4.3 - Prob. 101ECh. 4.3 - Prob. 102ECh. 4.3 - Prob. 103ECh. 4.3 - Prob. 104ECh. 4.3 - Prob. 105ECh. 4.3 - Prob. 106ECh. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 1-50, calculate the derivate of the...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 51-66, compute the indicated...Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - In Exercises 67-74, find the indicated derivative....Ch. 4.4 - Crude Oil Prices The price per barrel of crude oil...Ch. 4.4 - Median Home Prices The median home price in the...Ch. 4.4 - Marginal Profit Your monthly profit (in dollars)...Ch. 4.4 - Prob. 78ECh. 4.4 - Fuel Economy (You saw this exercise in Section...Ch. 4.4 - Fuel Economy (You saw this exercise in Section...Ch. 4.4 - Marginal Profit Paramount Electronics has an...Ch. 4.4 - Marginal Profit Refer back to Exercise 81. The...Ch. 4.4 - Food versus Education The percentage y (of total...Ch. 4.4 - Prob. 84ECh. 4.4 - Marginal Revenue The weekly revenue from the sale...Ch. 4.4 - Marginal Revenue The weekly revenue from the sale...Ch. 4.4 - Crime Statistics The murder rate in large cities...Ch. 4.4 - Crime Statistics Following is a quadratic model...Ch. 4.4 - Existing Home Sales The following graph shows the...Ch. 4.4 - Existing Home Sales Leading to the Financial...Ch. 4.4 - Pollution An offshore oil well is leaking oil and...Ch. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.4 - Revenue Growth The demand for the Cyberpunk II...Ch. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Say why the following was marked wrong, and give...Ch. 4.4 - Say why the following was marked wrong, and give...Ch. 4.4 - Name two major errors in the following graded test...Ch. 4.4 - Name two major errors in the following graded test...Ch. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - Prob. 2ECh. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...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 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - Research and Development: Industry The total spent...Ch. 4.5 - Research and Development: Federal The total spent...Ch. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Carbon Dating The age in years of a specimen that...Ch. 4.5 - Prob. 84ECh. 4.5 - New York City Housing Costs: Downtown The average...Ch. 4.5 - New York City Housing Costs: Uptown The average...Ch. 4.5 - Big Brother The following chart shows the total...Ch. 4.5 - Big Brother The following chart shows the total...Ch. 4.5 - Investments If $10,000 is invested in a savings...Ch. 4.5 - Investments If $20,000 is invested in a savings...Ch. 4.5 - Investments If $10,000 is invested in a savings...Ch. 4.5 - Investments If $20,000 is invested in a savings...Ch. 4.5 - Prob. 93ECh. 4.5 - The 2003 SARS Outbreak A few weeks into the deadly...Ch. 4.5 - Prob. 95ECh. 4.5 - Prob. 96ECh. 4.5 - Prob. 97ECh. 4.5 - SAT Scores by Income The following bar graph shows...Ch. 4.5 - Prob. 99ECh. 4.5 - Prob. 100ECh. 4.5 - Epidemics A flu epidemic described in Example 1 in...Ch. 4.5 - Prob. 102ECh. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4.5 - Prob. 105ECh. 4.5 - Subprime Mortgage Debt during the Housing Bubble...Ch. 4.5 - Prob. 107ECh. 4.5 - Prob. 108ECh. 4.5 - Radioactive Decay Plutonium 239 has a half-life of...Ch. 4.5 - Radioactive Decay Carbon 14 has a half-life of...Ch. 4.5 - Cellphone Revenues The number of cellphone...Ch. 4.5 - Cellphone Revenues The annual revenue for...Ch. 4.5 - Complete the following: The derivative of e raised...Ch. 4.5 - Complete the following: The derivative of the...Ch. 4.5 - Complete the following: The derivative of 2 raised...Ch. 4.5 - Complete the following: The derivative of the base...Ch. 4.5 - What is wrong with the following?...Ch. 4.5 - What is wrong with the following? ddx22x=(2)22x X...Ch. 4.5 - What is wrong with the following? ddx32x=(2x)32x1...Ch. 4.5 - Prob. 120ECh. 4.5 - Prob. 121ECh. 4.5 - Prob. 122ECh. 4.5 - Prob. 123ECh. 4.5 - Prob. 124ECh. 4.5 - Prob. 125ECh. 4.5 - Prob. 126ECh. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - Prob. 2ECh. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - Prob. 9ECh. 4.6 - Prob. 10ECh. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - Prob. 23ECh. 4.6 - Prob. 24ECh. 4.6 - Prob. 25ECh. 4.6 - Prob. 26ECh. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - Productivity The number of CDs per hour that...Ch. 4.6 - Productivity The number of cellphone accessory...Ch. 4.6 - Demand The demand equation for soccer tournament...Ch. 4.6 - Cost Equations The cost C (in cents) of producing...Ch. 4.6 - Housing Costs61 The cost C (in dollars) of...Ch. 4.6 - Employment An employment research company...Ch. 4.6 - Grades62 A productivity formula for a students...Ch. 4.6 - Grades Repeat Exercise 59 using the following...Ch. 4.6 - Exercises 61 and 62 are based on the following...Ch. 4.6 - Exercises 61 and 62 are based on the following...Ch. 4.6 - Fill in the missing terms: The equation x=y3+y3...Ch. 4.6 - Fill in the missing terms: When x0 in the equation...Ch. 4.6 - Use logarithmic differentiation to give another...Ch. 4.6 - Prob. 66ECh. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 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 - Prob. 21RECh. 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 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - In Exercises 47-52, find the equation of the...Ch. 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 - Sales OHaganBooks.com fits the cubic curve...Ch. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Cost OHaganBooks.com has been experiencing a run...Ch. 4 - Revenue At the moment, OHaganBooks.com is selling...Ch. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Website Activity The number of hits on...Ch. 4 - Prob. 70RECh. 4 - Demand and Revenue The price p that...Ch. 4 - Prob. 72RECh. 4 - Prob. 3CS
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- 3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE : 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50 KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8 KNm, 0, 30, 69.1, 68.1, 0 kNm.]arrow_forward4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward
- 7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward
- 1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả B X C d) ẢB°C e) ẢX B XC.arrow_forward3.13 (B). A beam ABC, 6 m long, is simply-supported at the left-hand end A and at B I'm from the right-hand end C. The beam is of weight 100 N/metre run. (a) Determine the reactions at A and B. (b) Construct to scales of 20 mm = 1 m and 20 mm = 100 N, the shearing-force diagram for the beam, indicating thereon the principal values. (c) Determine the magnitude and position of the maximum bending moment. (You may, if you so wish, deduce the answers from the shearing force diagram without constructing a full or partial bending-moment diagram.) [C.G.] C240 N, 360 N, 288 Nm, 2.4 m from A.]arrow_forward5. Using parentheses make sense of the expression V · VXVV · Å where Ả = Ã(x, y, z). Is the result a vector or a scaler?arrow_forward
- 3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20 KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m. Calculate the value of the reactions at A and D and hence draw the S.F. and B.M. diagrams. What are the magnitude and position of the maximum B.M. on the beam? [41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J m,arrow_forward3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A, a second concentrated load of 20 KN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine: (a) the values of the reactions at B and 0, (6) the position and magnitude of the maximum bending moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]arrow_forward3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward
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