 13.1: In Exercises 1 and 2, find and simplify the function values.
 13.2: In Exercises 1 and 2, find and simplify the function values.
 13.3: In Exercises 3 and 4, find the domain and range of the function.
 13.4: In Exercises 3 and 4, find the domain and range of the function.
 13.5: In Exercises 5 and 6, describe the level curves of the function. Sk...
 13.6: In Exercises 5 and 6, describe the level curves of the function. Sk...
 13.7: Consider the function (a) Sketch the graph of the surface given by ...
 13.8: A principal of $2000 is deposited in a savings account that earns i...
 13.9: In Exercises 9 and 10, sketch the graph of the level surface at the...
 13.10: In Exercises 9 and 10, sketch the graph of the level surface at the...
 13.11: In Exercises 1114, find the limit (if it exists) and discuss the co...
 13.12: In Exercises 1114, find the limit (if it exists) and discuss the co...
 13.13: In Exercises 1114, find the limit (if it exists) and discuss the co...
 13.14: In Exercises 1114, find the limit (if it exists) and discuss the co...
 13.15: In Exercises 1522, find all first partial derivatives.
 13.16: In Exercises 1522, find all first partial derivatives.
 13.17: In Exercises 1522, find all first partial derivatives.
 13.18: In Exercises 1522, find all first partial derivatives.
 13.19: In Exercises 1522, find all first partial derivatives.
 13.20: In Exercises 1522, find all first partial derivatives.
 13.21: In Exercises 1522, find all first partial derivatives.
 13.22: In Exercises 1522, find all first partial derivatives.
 13.23: In Exercises 2326, find the four second partial derivatives. Observ...
 13.24: In Exercises 2326, find the four second partial derivatives. Observ...
 13.25: In Exercises 2326, find the four second partial derivatives. Observ...
 13.26: In Exercises 2326, find the four second partial derivatives. Observ...
 13.27: Find the slopes of the surface in the  and directions at the point
 13.28: A company has two plants that produce the same lawn mower. If and a...
 13.29: In Exercises 2932, find the total differential.
 13.30: In Exercises 2932, find the total differential.
 13.31: In Exercises 2932, find the total differential.
 13.32: In Exercises 2932, find the total differential.
 13.33: In Exercises 33 and 34, (a) evaluate and and calculate and (b) use ...
 13.34: In Exercises 33 and 34, (a) evaluate and and calculate and (b) use ...
 13.35: The possible error involved in measuring each dimension of a right ...
 13.36: Approximate the propagated error and the relative error in the comp...
 13.37: In Exercises 37 and 38, find (a) by using the appropriate Chain Rul...
 13.38: In Exercises 37 and 38, find (a) by using the appropriate Chain Rul...
 13.39: In Exercises 39 and 40, find and (a) by using the appropriate Chain...
 13.40: In Exercises 39 and 40, find and (a) by using the appropriate Chain...
 13.41: In Exercises 41 and 42, differentiate implicitly to find the first ...
 13.42: In Exercises 41 and 42, differentiate implicitly to find the first ...
 13.43: In Exercises 43 and 44, use Theorem 13.9 to find the directional de...
 13.44: In Exercises 43 and 44, use Theorem 13.9 to find the directional de...
 13.45: In Exercises 45 and 46, use the gradient to find the directional de...
 13.46: In Exercises 45 and 46, use the gradient to find the directional de...
 13.47: In Exercises 4750, find the gradient of the function and the maximu...
 13.48: In Exercises 4750, find the gradient of the function and the maximu...
 13.49: In Exercises 4750, find the gradient of the function and the maximu...
 13.50: In Exercises 4750, find the gradient of the function and the maximu...
 13.51: In Exercises 51 and 52, (a) find the gradient of the function at (b...
 13.52: In Exercises 51 and 52, (a) find the gradient of the function at (b...
 13.53: In Exercises 5356, find an equation of the tangent plane to the sur...
 13.54: In Exercises 5356, find an equation of the tangent plane to the sur...
 13.55: In Exercises 5356, find an equation of the tangent plane to the sur...
 13.56: In Exercises 5356, find an equation of the tangent plane to the sur...
 13.57: In Exercises 57 and 58, find an equation of the tangent plane and f...
 13.58: In Exercises 57 and 58, find an equation of the tangent plane and f...
 13.59: Find the angle of inclination of the tangent plane to the surface a...
 13.60: Consider the following approximations for a function centered at Li...
 13.61: In Exercises 6166, examine the function for relative extrema and sa...
 13.62: In Exercises 6166, examine the function for relative extrema and sa...
 13.63: In Exercises 6166, examine the function for relative extrema and sa...
 13.64: In Exercises 6166, examine the function for relative extrema and sa...
 13.65: In Exercises 6166, examine the function for relative extrema and sa...
 13.66: In Exercises 6166, examine the function for relative extrema and sa...
 13.67: Find the minimum distance from the point to the surface Hint: To si...
 13.68: Find three positive integers, and such that the product is 64 and t...
 13.69: A company manufactures two types of bicycles, a racing bicycle and ...
 13.70: A corporation manufactures digital cameras at two locations. The co...
 13.71: In Exercises 71 and 72, find the least squares regression line for ...
 13.72: In Exercises 71 and 72, find the least squares regression line for ...
 13.73: An agronomist used four test plots to determine the relationship be...
 13.74: The data in the table show the yield (in milligrams) of a chemical ...
 13.75: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.76: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.77: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.78: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.79: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.80: In Exercises 7580, use Lagrange multipliers to find the indicated e...
 13.81: A water line is to be built from point to point and must pass throu...
Solutions for Chapter 13: Functions of Several Variables
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 13: Functions of Several Variables
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Chapter 13: Functions of Several Variables includes 81 full stepbystep solutions. Since 81 problems in chapter 13: Functions of Several Variables have been answered, more than 18419 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendental Functions was written by Sieva Kozinsky and is associated to the ISBN: 9781285774770. This expansive textbook survival guide covers the following chapters and their solutions.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Compounded monthly
See Compounded k times per year.

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Irrational zeros
Zeros of a function that are irrational numbers.

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Minute
Angle measure equal to 1/60 of a degree.

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Real part of a complex number
See Complex number.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Sine
The function y = sin x.

Terminal point
See Arrow.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Vertical translation
A shift of a graph up or down.

zaxis
Usually the third dimension in Cartesian space.
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