Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
15th Edition
ISBN: 9780137590728
Author: Larry Goldstein, David Lay
Publisher: PEARSON+
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Chapter 7.5, Problem 14E
(a)
To determine
The least square line for the data for number of visitors per year at Yosemite National Park given below in the table using,
Partial derivative method
Formulas
(b)
To determine
The number of visitors per year at Yosemite National Park in the year2017 for the data given in the table below,
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1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
Chapter 7 Solutions
Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
Ch. 7.1 - Let f(x,y,z)=x2+y(xz)4. Compute f(3,5,2).Ch. 7.1 - Prob. 2CYUCh. 7.1 - Let f(x,y)=x23xyy2. Compute f(5,0),f(5,2) and...Ch. 7.1 - Prob. 2ECh. 7.1 - Let g(x,y,z)=x/(yz). Compute g(1,1),g(0,1) and...Ch. 7.1 - Let f(x,y,z)=x2ey2+z2. Compute f(1,1,1) and...Ch. 7.1 - Let f(x,y)=xy. Show that f(2+h,3)f(2,3)=3h.Ch. 7.1 - Let f(x,y)=xy. Show that f(2,3+k)f(2,3)=2k.Ch. 7.1 - Cost Find a formula C(x,y,z) that gives the cost...Ch. 7.1 - Cost Find a formula C(x,y,z) that gives the cost...
Ch. 7.1 - Consider the cobb-Douglas production function...Ch. 7.1 - Let f(x,y)=10x25y35. Show that f(3a,3b)=3f(a,b).Ch. 7.1 - Present value The present value of A dollars to be...Ch. 7.1 - Refer to Example 3. If labor costs $100 per unit...Ch. 7.1 - Tax and Homeowner Exemption The value of...Ch. 7.1 - Tax and Homeowner Exemption Let f(r,v,x) be the...Ch. 7.1 - Draw the level curve of height 0,1 and 2 for the...Ch. 7.1 - Draw the level curve of height 0,1 and 2 for the...Ch. 7.1 - Draw the level curve of function f(x,y)=xy...Ch. 7.1 - Draw the level curve of function f(x,y)=xy...Ch. 7.1 - Find the function f(x,y) that has line y=3x4 as a...Ch. 7.1 - Find the function f(x,y) that has the curve y=2x2...Ch. 7.1 - Suppose that a topographic map is viewed as the...Ch. 7.1 - Isocost Lines A certain production process uses...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.2 - The number of TV sets an appliance store sells per...Ch. 7.2 - The monthly mortgage payment for a house is a...Ch. 7.2 - Find fxandfy for each of the following functions....Ch. 7.2 - Prob. 2ECh. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Prob. 6ECh. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Prob. 13ECh. 7.2 - Let f(p,q)=1p(1+q). Find fq and fp.Ch. 7.2 - Let f(x,y,z)=(1+x2y)/z. fx,fy,andfz.Ch. 7.2 - Prob. 16ECh. 7.2 - Let f(x,y,z)=xzeyz. Find fx,fy,andfz.Ch. 7.2 - Let f(x,y,z)=xyz. Find fx,fz,andfz.Ch. 7.2 - Let f(x,y,z)=x2+2xy+y2+3x+5y. Find...Ch. 7.2 - Prob. 20ECh. 7.2 - Let f(x,y)=xy2+5. Evaluate fy at (x,y)=(2,1) and...Ch. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - ProductivityLabor and Capital The productivity of...Ch. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Let p1 be the average price of MP3 players, p2 the...Ch. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Compute 2fy2, where f(x,y)=60x3/4y1/4, a...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.3 - Prob. 1CYUCh. 7.3 - Prob. 2CYUCh. 7.3 - Prob. 1ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 17ECh. 7.3 - The function f(x,y)=12x2+2xy+9+3y2x+2y has a...Ch. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 27ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 36ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Minimizing Surface Area Find the dimensions of the...Ch. 7.3 - Maximizing Profit A company manufactures and sells...Ch. 7.3 - Maximizing Profit A monopolist manufactures and...Ch. 7.3 - Prob. 53ECh. 7.3 - Revenue from Two Products A company manufactures...Ch. 7.4 - Prob. 1CYUCh. 7.4 - Refer to Exercise 29 of Section 7.3. What is the...Ch. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 19ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Use Lagrange multipliers to find the three...Ch. 7.4 - Minimizing Surface Area Find the dimensions of an...Ch. 7.4 - Maximizing Volume A shelter for use at the beach...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.5 - Prob. 1CYUCh. 7.5 - Prob. 2CYUCh. 7.5 - Prob. 1ECh. 7.5 - Find the least-squares error E for the...Ch. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - In the remaining exercises, use one or more of the...Ch. 7.5 - In the remaining exercises, use one or more of the...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.6 - Calculate the iterated integral 02(0x/2e2yxdy)dx.Ch. 7.6 - Prob. 2CYUCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Prob. 5ECh. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Calculate the volumes over the following regions R...Ch. 7 - Give an example of a level curve of a function of...Ch. 7 - Prob. 2FCCECh. 7 - Prob. 3FCCECh. 7 - Prob. 4FCCECh. 7 - Prob. 5FCCECh. 7 - Prob. 6FCCECh. 7 - Prob. 7FCCECh. 7 - Prob. 8FCCECh. 7 - Prob. 9FCCECh. 7 - Prob. 10FCCECh. 7 - Prob. 11FCCECh. 7 - Prob. 12FCCECh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Let fx,y=2x3+x2yy2. Compute 2fx2,2fy2, and 2fxy at...Ch. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - In Exercises 1720, find all points (x,y) where...Ch. 7 - Prob. 19RECh. 7 - In Exercises 1720, find all points (x,y) where...Ch. 7 - In Exercises 2123, find all points (x,y) where...Ch. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Find the values of x,y,z at which...Ch. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Use the method of Lagrange multiplier to: A person...Ch. 7 - Use the method of Lagrange multiplier to: The...Ch. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RE
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