 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 47679 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.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Cotangent
The function y = cot x

Demand curve
p = g(x), where x represents demand and p represents price

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Elimination method
A method of solving a system of linear equations

Gaussian curve
See Normal curve.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Irrational zeros
Zeros of a function that are irrational numbers.

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Polar form of a complex number
See Trigonometric form of a complex number.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Zero matrix
A matrix consisting entirely of zeros.