 7.1: In Exercises 13, (a) plot the points on a threedimensional coordin...
 7.2: In Exercises 13, (a) plot the points on a threedimensional coordin...
 7.3: In Exercises 13, (a) plot the points on a threedimensional coordin...
 7.4: In Exercises 4 and 5, find the standard equation of the sphere. Cen...
 7.5: In Exercises 4 and 5, find the standard equation of the sphere. End...
 7.6: Find the center and radius of the sphere whose equation is x2 y2 z2...
 7.7: In Exercises 79, find the intercepts and sketch the graph of the pl...
 7.8: In Exercises 79, find the intercepts and sketch the graph of the pl...
 7.9: In Exercises 79, find the intercepts and sketch the graph of the pl...
 7.10: In Exercises 1012, identify the quadric surface.
 7.11: In Exercises 1012, identify the quadric surface.
 7.12: In Exercises 1012, identify the quadric surface.
 7.13: In Exercises 1315, find and
 7.14: In Exercises 1315, find and
 7.15: In Exercises 1315, find and
 7.16: The contour map shows level curves of equal temperature (isotherms)...
 7.17: In Exercises 17 and 18, find and and evaluate each at the point
 7.18: In Exercises 17 and 18, find and and evaluate each at the point
 7.19: In Exercises 19 and 20, find any critical points, relative extrema,...
 7.20: In Exercises 19 and 20, find any critical points, relative extrema,...
 7.21: A company manufactures two types of wood burning stoves: a freestan...
 7.22: Physical Science Assume that Earth is a sphere with a radius of 396...
 7.23: In Exercises 1926, identify the surface. z x2 9 y2
 7.24: In Exercises 1926, identify the surface. 4x2 y2 z2 4
 7.25: In Exercises 1926, identify the surface. z x2 y2
 7.26: In Exercises 1926, identify the surface. z 9x 3y 5
 7.27: In Exercises 27 and 28, find the function values.
 7.28: In Exercises 27 and 28, find the function values.
 7.29: n Exercises 29 and 30, describe the region in the plane that corre...
 7.30: n Exercises 29 and 30, describe the region in the plane that corre...
 7.31: In Exercises 3134, describe the level curves of the function. Sketc...
 7.32: In Exercises 3134, describe the level curves of the function. Sketc...
 7.33: In Exercises 3134, describe the level curves of the function. Sketc...
 7.34: In Exercises 3134, describe the level curves of the function. Sketc...
 7.35: Meteorology The contour map shown below represents the average year...
 7.36: Population Density The contour map below represents the population ...
 7.37: Chemistry The acidity of rainwater is measured in units called pH, ...
 7.38: Sales The table gives the sales (in billions of dollars), the share...
 7.39: Equation of Exchange Economists use an equation of exchange to expr...
 7.40: Biomechanics The Froude number defined asF v2 glwhere represents ve...
 7.41: In Exercises 4150, find all first partial derivatives. fx, y x2y 3x...
 7.42: In Exercises 4150, find all first partial derivatives. fx, y 4xy xy...
 7.43: In Exercises 4150, find all first partial derivatives. z x2 y2
 7.44: In Exercises 4150, find all first partial derivatives. z xy 2x 4y2
 7.45: In Exercises 4150, find all first partial derivatives. fx, y ln2x 3y
 7.46: In Exercises 4150, find all first partial derivatives. fx, y ln2x 3y
 7.47: In Exercises 4150, find all first partial derivatives. fx, y xey yex
 7.48: In Exercises 4150, find all first partial derivatives. fx, y x2e2y
 7.49: In Exercises 4150, find all first partial derivatives. w xyz2
 7.50: In Exercises 4150, find all first partial derivatives. w 3xy 5xz 2yz
 7.51: In Exercises 5154, find the slope of the surface at the indicated p...
 7.52: In Exercises 5154, find the slope of the surface at the indicated p...
 7.53: In Exercises 5154, find the slope of the surface at the indicated p...
 7.54: In Exercises 5154, find the slope of the surface at the indicated p...
 7.55: In Exercises 5558, find all second partial derivatives.
 7.56: In Exercises 5558, find all second partial derivatives.
 7.57: In Exercises 5558, find all second partial derivatives.
 7.58: In Exercises 5558, find all second partial derivatives.
 7.59: Marginal Cost A company manufactures two models of skis:crosscount...
 7.60: Marginal Revenue At a baseball stadium, souvenir caps are sold at t...
 7.61: Medical Science The surface area of an average human body in square...
 7.62: Medicine In order to treat a certain bacterial infection, a combina...
 7.63: In Exercises 6370, find any critical points and relative extrema of...
 7.64: In Exercises 6370, find any critical points and relative extrema of...
 7.65: In Exercises 6370, find any critical points and relative extrema of...
 7.66: In Exercises 6370, find any critical points and relative extrema of...
 7.67: In Exercises 6370, find any critical points and relative extrema of...
 7.68: In Exercises 6370, find any critical points and relative extrema of...
 7.69: In Exercises 6370, find any critical points and relative extrema of...
 7.70: In Exercises 6370, find any critical points and relative extrema of...
 7.71: Revenue A company manufactures and sells two products. The demand f...
 7.72: Profit A company manufactures a product at two different locations....
 7.73: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.74: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.75: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.76: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.77: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.78: In Exercises 7378, locate any extrema of the function by using Lagr...
 7.79: In Exercises 79 and 80, use a spreadsheet to find the indicated ext...
 7.80: In Exercises 79 and 80, use a spreadsheet to find the indicated ext...
 7.81: Maximum Production Level The production function for a manufacturer...
 7.82: Minimum Cost A manufacturer has an order for 1000 units of wooden b...
 7.83: In Exercises 83 and 84, (a) use the method of least squares to find...
 7.84: In Exercises 83 and 84, (a) use the method of least squares to find...
 7.85: Agriculture An agronomist used four test plots to determine the rel...
 7.86: Work Force The table gives the percents and numbers (in millions) o...
 7.87: In Exercises 87 and 88, use the regression capabilities of a graphi...
 7.88: In Exercises 87 and 88, use the regression capabilities of a graphi...
 7.89: In Exercises 8992, evaluate the double integral.1 01x 0 4x 2y dy dx
 7.90: In Exercises 8992, evaluate the double integral.3 34 0 x y2 dx dy
 7.91: In Exercises 8992, evaluate the double integral. 2 12y 1 x y2 dx dy
 7.92: In Exercises 8992, evaluate the double integral.4 016x2 0 2x dy dx
 7.93: In Exercises 9396, use a double integral to find the area of the re...
 7.94: In Exercises 9396, use a double integral to find the area of the re...
 7.95: In Exercises 9396, use a double integral to find the area of the re...
 7.96: In Exercises 9396, use a double integral to find the area of the re...
 7.97: Find the volume of the solid bounded by the graphs of and
 7.98: Find the volume of the solid bounded by the graphs of and
 7.99: Average Elevation In a triangular coastal area, the elevation in mi...
 7.100: Real Estate The value of real estate (in dollars per square foot) f...
Solutions for Chapter 7: Functions of Several Variables
Full solutions for Calculus: An Applied Approach  8th Edition
ISBN: 9780618958252
Solutions for Chapter 7: Functions of Several Variables
Get Full SolutionsSince 100 problems in chapter 7: Functions of Several Variables have been answered, more than 23649 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7: Functions of Several Variables includes 100 full stepbystep solutions. Calculus: An Applied Approach was written by and is associated to the ISBN: 9780618958252. This textbook survival guide was created for the textbook: Calculus: An Applied Approach , edition: 8.

Bearing
Measure of the clockwise angle that the line of travel makes with due north

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Constant
A letter or symbol that stands for a specific number,

Division
a b = aa 1 b b, b Z 0

Graphical model
A visible representation of a numerical or algebraic model.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Law of sines
sin A a = sin B b = sin C c

Natural logarithm
A logarithm with base e.

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Quotient polynomial
See Division algorithm for polynomials.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Rational expression
An expression that can be written as a ratio of two polynomials.

Resistant measure
A statistical measure that does not change much in response to outliers.

Right triangle
A triangle with a 90° angle.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Vertical component
See Component form of a vector.