 14.1.1: . In Example 2 we considered the function , where W is the windchi...
 14.1.2: The temperaturehumidity index (or humidex, for short) is the perce...
 14.1.3: A manufacturer has modeled its yearly production function (the mone...
 14.1.4: Verify for the CobbDouglas production function discussed in Exampl...
 14.1.5: A model for the surface area of a human body is given by the functi...
 14.1.6: The windchill index discussed in Example 2 has been modeled by the...
 14.1.7: The wave heights h in the open sea depend on the speed of the wind ...
 14.1.8: A company makes three sizes of cardboard boxes: small, medium, and ...
 14.1.9: Let . (a) Evaluate . (b) Find the domain of . (c) Find the range of .
 14.1.10: Let . (a) Evaluate . (b) Find and sketch the domain of . (c) Find t...
 14.1.11: Let . (a) Evaluate . (b) Find and describe the domain of .
 14.1.12: Let . (a) Evaluate . (b) Find and describe the domain of .
 14.1.13: 1322 Find and sketch the domain of the function.fx, y s2x y f x
 14.1.14: 1322 Find and sketch the domain of the function.f x, y sxyfx
 14.1.15: 1322 Find and sketch the domain of the function.fx, y ln9 x 2 9y2f x,
 14.1.16: 1322 Find and sketch the domain of the function.fx, y sx 2 y 2 fx,
 14.1.17: 1322 Find and sketch the domain of the function.f x, y s1 x 2 s1 y 2f
 14.1.18: 1322 Find and sketch the domain of the function.f x, y sy s25 x 2 y...
 14.1.19: 1322 Find and sketch the domain of the function. x, y sy x 21 x 2f
 14.1.20: 1322 Find and sketch the domain of the function.f x, y arcsinx 2 y ...
 14.1.21: 1322 Find and sketch the domain of the function.f x, y, z s1 x 2 y ...
 14.1.22: 1322 Find and sketch the domain of the function.f x, y, z ln16 4x 2...
 14.1.23: 2331 Sketch the graph of the function.fx, y 1 y fx,
 14.1.24: 2331 Sketch the graph of the function.fx, y 2 xfx
 14.1.25: 2331 Sketch the graph of the function.f x, y 10 4x 5yfx
 14.1.26: 2331 Sketch the graph of the function.fx, y ey f x
 14.1.27: 2331 Sketch the graph of the function.f x, y y 2 1fx,
 14.1.28: 2331 Sketch the graph of the function.fx, y 1 2x 2 2y 2 f x,
 14.1.29: 2331 Sketch the graph of the function.fx, y 9 x 2 9y 2fx
 14.1.30: 2331 Sketch the graph of the function.fx, y s4x 2 y 2 fx,
 14.1.31: 2331 Sketch the graph of the function.fx, y s4 4x 2 y 2f
 14.1.32: Match the function with its graph (labeled IVI). Give reasons for y...
 14.1.33: A contour map for a function is shown. Use it to esti mate the valu...
 14.1.34: Shown is a contour map of atmospheric pressure in North America on ...
 14.1.35: . Level curves (isothermals) are shown for the water temperature in...
 14.1.36: Two contour maps are shown. One is for a function whose graph is a ...
 14.1.37: . Locate the points and on the map of Lonesome Mountain (Figure 12)...
 14.1.38: Make a rough sketch of a contour map for the function whose graph i...
 14.1.39: 39 42 A contour map of a function is shown. Use it to make a rough ...
 14.1.40: 39 42 A contour map of a function is shown. Use it to make a rough ...
 14.1.41: 39 42 A contour map of a function is shown. Use it to make a rough ...
 14.1.42: 39 42 A contour map of a function is shown. Use it to make a rough ...
 14.1.43: 4350 Draw a contour map of the function showing several level curve...
 14.1.44: 4350 Draw a contour map of the function showing several level curve...
 14.1.45: 4350 Draw a contour map of the function showing several level curve...
 14.1.46: 4350 Draw a contour map of the function showing several level curve...
 14.1.47: 4350 Draw a contour map of the function showing several level curve...
 14.1.48: 4350 Draw a contour map of the function showing several level curve...
 14.1.49: 4350 Draw a contour map of the function showing several level curve...
 14.1.50: 4350 Draw a contour map of the function showing several level curve...
 14.1.51: 5152 Sketch both a contour map and a graph of the function and comp...
 14.1.52: 5152 Sketch both a contour map and a graph of the function and comp...
 14.1.53: A thin metal plate, located in the plane, has temperature at the p...
 14.1.54: If is the electric potential at a point in the plane, then the lev...
 14.1.55: 5558 Use a computer to graph the function using various domains and...
 14.1.56: 5558 Use a computer to graph the function using various domains and...
 14.1.57: 5558 Use a computer to graph the function using various domains and...
 14.1.58: 5558 Use a computer to graph the function using various domains and...
 14.1.59: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.60: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.61: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.62: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.63: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.64: 5964 Match the function (a) with its graph (labeled AF below) and (...
 14.1.65: 6568 Describe the level surfaces of the function.f x, y, z x 3y 5zf x,
 14.1.66: 6568 Describe the level surfaces of the function.f x, y, z x 2 3y 2...
 14.1.67: 6568 Describe the level surfaces of the function.f x, y, z y 2 z2f x,
 14.1.68: 6568 Describe the level surfaces of the function.f x, y, z x 2 y 2 z2t
 14.1.69: 6970 Describe how the graph of is obtained from the graph oftx, y f...
 14.1.70: 6970 Describe how the graph of is obtained from the graph oftx, y f...
 14.1.71: 7172 Use a computer to graph the function using various domains and...
 14.1.72: 7172 Use a computer to graph the function using various domains and...
 14.1.73: 7374 Use a computer to graph the function using various domains and...
 14.1.74: 7374 Use a computer to graph the function using various domains and...
 14.1.75: Use a computer to investigate the family of functions. How does the...
 14.1.76: Use a computer to investigate the family of surfacesHow does the sh...
 14.1.77: Use a computer to investigate the family of surfaces . In particula...
 14.1.78: Graph the functions and In general, if t is a function of one varia...
 14.1.79: (a) Show that, by taking logarithms, the general CobbDouglas functi...
Solutions for Chapter 14.1: Functions of Several Variables
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 14.1: Functions of Several Variables
Get Full SolutionsSince 79 problems in chapter 14.1: Functions of Several Variables have been answered, more than 31470 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 14.1: Functions of Several Variables includes 79 full stepbystep solutions.

Arccosecant function
See Inverse cosecant function.

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

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

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Implied domain
The domain of a function’s algebraic expression.

Inverse variation
See Power function.

Measure of an angle
The number of degrees or radians in an angle

Multiplication property of equality
If u = v and w = z, then uw = vz

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Parameter
See Parametric equations.

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Parametrization
A set of parametric equations for a curve.

Projectile motion
The movement of an object that is subject only to the force of gravity

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Trigonometric form of a complex number
r(cos ? + i sin ?)

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

xintercept
A point that lies on both the graph and the xaxis,.