 2.1: The component functions of a vectorvalued function are vectors.
 2.2: The domain of f(x, y) = x 2 + y2 + 1, 3 x + y , x y is {(x, y) R2 ...
 2.3: The range of f(x, y) = x 2 + y2 + 1, 3 x + y , x y is {(u, v, w) R3...
 2.4: The function f: R3 {(0, 0, 0)} R3, f(x) = 2x/x is oneone.
 2.5: The graph of x = 9y2 + z2/4 is a paraboloid.
 2.6: The graph of z + x 2 = y2 is a hyperboloid.
 2.7: The level set of a function f (x, y,z) is either empty or a surface.
 2.8: The graph of any function of two variables is a level set of a func...
 2.9: The level set of any function of three variables is the graph of a ...
 2.10: lim (x,y)(0,0) x 2 2y2 x 2 + y2 = 1.
 2.11: If f (x, y) = y4 x 4 x 2 + y2 when (x, y) = (0, 0) 2 when (x, y) = ...
 2.12: If f (x, y) approaches a number L as (x, y) (a, b) along all lines ...
 2.13: If limxa f(x) exists and is finite, then f is continuous at a.
 2.14: fx (a, b) = lim xa f (x, b) f (a, b) x a .
 2.15: If f (x, y,z) = sin y, then f (x, y,z) = cos y.
 2.16: If f: R3 R4 is differentiable, then Df(x) is a 3 4 matrix.
 2.17: If f is differentiable at a, then f is continuous at a.
 2.18: If f is continuous at a, then f is differentiable at a
 2.19: If all partial derivatives f/x1,..., f/xn of a function f (x1,..., ...
 2.20: If f: R4 R5 and g: R4 R5 are both differentiable at a R4, then D(f ...
 2.21: Theres a function f of class C2 such that f x = y3 2x and f y = y 3...
 2.22: If the secondorder partial derivatives of f exist at (a, b), then ...
 2.23: If w = F(x, y,z) and z = g(x, y) where F and g are differentiable, ...
 2.24: The tangent plane to z = x 3/(y + 1) at the point (2, 0, 8) has equ...
 2.25: The plane tangent to x y/z2 = 1 at (2, 8, 4) has equation 4x + y + ...
 2.26: The plane tangent to the surface x 2 + xyez + y3 = 1 at the point (...
 2.27: Dj f (x, y,z) = f y
 2.28: Dk f (x, y,z) = f z .
 2.29: If f (x, y) = sin x cos y and v is a unit vector in R2, then 0 Dv f...
 2.30: If v is a unit vector in R3 and f (x, y,z) = sin x cos y + sin z, t...
 2.31: Use the function f (x, y,z) = x yz and the multivariable chain rule...
 2.32: Suppose that f : Rn R is a function of class C2. The Laplacian of f...
 2.33: (a) Consider a function f (x, y) of class C4. Show that if we apply...
 2.34: Livinia, the housefly, finds herself caught in the oven at the poin...
 2.35: Consider the surface given in cylindrical coordinates by the equati...
 2.36: The partial differential equation 2u x 2 + 2u y2 + 2u z2 = c 2u t 2...
 2.37: Let X be an open set in Rn. A function F: X R is said to be homogen...
 2.38: Let X be an open set in Rn. A function F: X R is said to be homogen...
 2.39: Let X be an open set in Rn. A function F: X R is said to be homogen...
 2.40: Let X be an open set in Rn. A function F: X R is said to be homogen...
 2.41: Let X be an open set in Rn. A function F: X R is said to be homogen...
 2.42: If F(x, y,z) is a polynomial, characterize what it means to say tha...
 2.43: Suppose F(x1, x2,..., xn) is differentiable and homogeneous of degr...
 2.44: Generalize Eulers formula as follows: If F is of class C2 and homog...
Solutions for Chapter 2: Differentiation in Several Variables
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 2: Differentiation in Several Variables
Get Full SolutionsThis textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Chapter 2: Differentiation in Several Variables includes 44 full stepbystep solutions. Since 44 problems in chapter 2: Differentiation in Several Variables have been answered, more than 13399 students have viewed full stepbystep solutions from this chapter. Vector Calculus was written by and is associated to the ISBN: 9780321780652. 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.

Acute triangle
A triangle in which all angles measure less than 90°

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Exponential form
An equation written with exponents instead of logarithms.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

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

Inverse properties
a + 1a2 = 0, a # 1a

Irrational numbers
Real numbers that are not rational, p. 2.

Line of travel
The path along which an object travels

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Perihelion
The closest point to the Sun in a planet’s orbit.

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.

Polar equation
An equation in r and ?.

Reciprocal function
The function ƒ(x) = 1x

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Speed
The magnitude of the velocity vector, given by distance/time.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

Yscl
The scale of the tick marks on the yaxis in a viewing window.