Solutions for Chapter 14: Partial Derivatives

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

A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

See Power function.

A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.

See Ellipse, Hyperbola, Parabola.

limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

An expression of the form logb x (see Logarithmic function)

See Absolute value of a complex number.

A polynomial with exactly one term.

The function ƒ1x2 = ex.

The numbers 1, 2, 3, . . . ,.

An interval that does not include its endpoints.

The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Numbers that can be written as a/b, where a and b are integers, and b ? 0.

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

See Convergence of a series

The matrix AT obtained by interchanging the rows and columns of A.

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

The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.