Applied Calculus
7th Edition
ISBN: 9781337291248
Author: Waner, Stefan.
Publisher: Cengage Learning,
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Textbook Question
Chapter 6.4, Problem 68E
Bottled Water Sales (Compare Exercise 46 in Section 6.3.) The rate of U.S. per capita sales of bottled water for the period 2007–2014 can be approximated by
where t is time in years since the start of 2007. Use a definite
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
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(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
Chapter 6 Solutions
Applied Calculus
Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 20ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Find f(x) if f(0)=1 and the tangent line at...Ch. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Prob. 45ECh. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Facebook Membership At the start of 2010, Facebook...Ch. 6.1 - Uploads to YouTube Since YouTube first became...Ch. 6.1 - Median Household Income From 2000 to 2007, median...Ch. 6.1 - Mean Household Income From 2000 to 2007 the mean...Ch. 6.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.1 - Bottled Water Sales The rate of U.S. per capita...Ch. 6.1 - Health-Care Spending in the 1990s Write H(t) for...Ch. 6.1 - Health-Care Spending in the 2000s Write H(t) for...Ch. 6.1 - Prob. 59ECh. 6.1 - Subprime Mortgage Debt during the Housing Bubble...Ch. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.1 - Prob. 81ECh. 6.1 - If we know an antiderivative of a function, do we...Ch. 6.1 - Prob. 83ECh. 6.1 - Your friend Marco claims that once you have one...Ch. 6.1 - Prob. 85ECh. 6.1 - Prob. 86ECh. 6.1 - Prob. 87ECh. 6.1 - Prob. 88ECh. 6.1 - Prob. 89ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 91ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 93ECh. 6.1 - Prob. 94ECh. 6.1 - Prob. 95ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 97ECh. 6.1 - Prob. 98ECh. 6.1 - Prob. 99ECh. 6.1 - Prob. 100ECh. 6.1 - Prob. 101ECh. 6.1 - Prob. 102ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 37ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - In Exercises 5772, use the shortcut formulas (see...Ch. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Find f(x) if f(1)=0 and the tangent line at...Ch. 6.2 - Prob. 75ECh. 6.2 - Find f(x) if f(2)=1 and the tangent line at x has...Ch. 6.2 - Prob. 77ECh. 6.2 - Prob. 78ECh. 6.2 - Prob. 79ECh. 6.2 - Prob. 80ECh. 6.2 - Prob. 81ECh. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - Prob. 83ECh. 6.2 - Prob. 84ECh. 6.2 - Cost The marginal cost of producing the xth roll...Ch. 6.2 - Prob. 86ECh. 6.2 - Economic Growth The Mexico GDP (total monetary...Ch. 6.2 - Prob. 88ECh. 6.2 - Prob. 89ECh. 6.2 - Revenue: Google The annual revenue of Google Inc....Ch. 6.2 - Scientific Research: 19832003 The number of...Ch. 6.2 - Prob. 92ECh. 6.2 - Prob. 93ECh. 6.2 - Prob. 94ECh. 6.2 - Prob. 95ECh. 6.2 - Motion in a Straight Line The velocity of a...Ch. 6.2 - Bottled Water Sales (Compare Exercise 55 in...Ch. 6.2 - Prob. 98ECh. 6.2 - Prob. 99ECh. 6.2 - You are asked to calculate uu2+1du. What is wrong...Ch. 6.2 - Prob. 101ECh. 6.2 - Prob. 102ECh. 6.2 - Prob. 103ECh. 6.2 - If the substitution u=x21 works in xx21dx, why...Ch. 6.2 - Prob. 105ECh. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Prob. 107ECh. 6.2 - Prob. 108ECh. 6.2 - Prob. 109ECh. 6.2 - Prob. 110ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 3ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 5ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 22ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 25ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - Prob. 33ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Pumps A pump is delivering water into a tank at a...Ch. 6.3 - Cost The marginal cost function for the...Ch. 6.3 - Prob. 42ECh. 6.3 - Profit: iPhones Assume that Apples marginal cost...Ch. 6.3 - Profit: PlayStation 4s Assume that Sony's marginal...Ch. 6.3 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Online Auctions The following graph shows the rate...Ch. 6.3 - Prob. 49ECh. 6.3 - Scientific Research Exercises 49 and 50 are based...Ch. 6.3 - Graduate Degrees: Women The following graph shows...Ch. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Offshore Crude Oil Production: Mexico The...Ch. 6.3 - Prob. 59ECh. 6.3 - Motion under Gravity The velocity of a stone...Ch. 6.3 - Prob. 61ECh. 6.3 - Motion A race car has a velocity given by...Ch. 6.3 - Prob. 63ECh. 6.3 - Uploads to YouTube Since YouTube first became...Ch. 6.3 - Prob. 65ECh. 6.3 - Big Brother The number of wiretaps authorized each...Ch. 6.3 - Surveying My uncle intends to build a...Ch. 6.3 - Pollution An aerial photograph of an ocean oil...Ch. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - If f is an increasing function of x, then the left...Ch. 6.3 - If f is a decreasing function of x, then the left...Ch. 6.3 - Prob. 77ECh. 6.3 - Sketch the graphs of two (different) functions f...Ch. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - Prob. 87ECh. 6.3 - Prob. 88ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 28ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 41ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - Prob. 51ECh. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Profit: iPhones (Compare Exercise 43 in Section...Ch. 6.4 - Profit: PlayStation 4s (Compare Exercise 44 in...Ch. 6.4 - Prob. 61ECh. 6.4 - Motion A ball thrown in the air has a velocity of...Ch. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Fuel Consumption The way Professor Waner drives,...Ch. 6.4 - Fuel Consumption The way Professor Costenoble...Ch. 6.4 - Prob. 67ECh. 6.4 - Bottled Water Sales (Compare Exercise 46 in...Ch. 6.4 - Prob. 69ECh. 6.4 - Uploads to YouTube (Compare Exercise 64 in Section...Ch. 6.4 - Big Brother (Compare Exercise 65 in Section 6.3.)...Ch. 6.4 - Big Brother (Compare Exercise 66 in Section 6.3.)...Ch. 6.4 - Prob. 73ECh. 6.4 - Housing Starts: The Great Recession (Compare...Ch. 6.4 - Sales Weekly sales of your Lord of the Rings...Ch. 6.4 - Sales Annual sales of fountain pens in Littleville...Ch. 6.4 - Prob. 77ECh. 6.4 - Embryo Development The oxygen consumption of a...Ch. 6.4 - Prob. 79ECh. 6.4 - Online Auctions The rate of change n(t) of the...Ch. 6.4 - Prob. 81ECh. 6.4 - Cost The total cost of producing x items is given...Ch. 6.4 - Prob. 83ECh. 6.4 - Scientific Research: 19832003 (Compare Exercise 92...Ch. 6.4 - Prob. 85ECh. 6.4 - The Logistic Function and Grant Spending a. Show...Ch. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - What is definite about the definite integral?Ch. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 95ECh. 6.4 - Prob. 96ECh. 6.4 - Prob. 97ECh. 6.4 - Explain why, in computing the total change of a...Ch. 6.4 - Prob. 99ECh. 6.4 - Prob. 100ECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 2RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 4RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 6RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 8RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 10RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 12RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 14RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - In Exercises 19 and 20, use the given graph to...Ch. 6 - Prob. 20RECh. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - Prob. 26RECh. 6 - In Exercises 27 and 28, use technology to...Ch. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 34RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 36RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 38RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Sales At OHaganBooks.com, the rate of net sales...Ch. 6 - Prob. 46RECh. 6 - Motion under Gravity Billy-Sean OHagans friend...Ch. 6 - Prob. 48RECh. 6 - Projected Sales Before OHaganBooks.com launched...Ch. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Sales The following graph shows the approximate...Ch. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 3CS
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Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
03a: Numerical Differentiation Review; Author: Jaisohn Kim;https://www.youtube.com/watch?v=IMYsqbV4CEg;License: Standard YouTube License, CC-BY