 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 31518 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. This expansive textbook survival guide covers the following chapters and their solutions.

Central angle
An angle whose vertex is the center of a circle

Complex conjugates
Complex numbers a + bi and a  bi

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Divisor of a polynomial
See Division algorithm for polynomials.

Equilibrium price
See Equilibrium point.

Event
A subset of a sample space.

Explanatory variable
A variable that affects a response variable.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Perpendicular lines
Two lines that are at right angles to each other

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Radicand
See Radical.

Range (in statistics)
The difference between the greatest and least values in a data set.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Translation
See Horizontal translation, Vertical translation.