Solutions for Chapter 3: The Derivative

The notation PQ denoting the directed line segment with initial point P and terminal point Q.

A stemplot with leaves on either side used to compare two distributions.

See Exponential function, Logarithmic function, nth power of a.

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

See Ellipse, Hyperbola, Parabola.

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

See Complex number.

The composition of a one-toone function with its inverse results in the identity function.

limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

See Magnitude of a vector.

The sum of all the data divided by the total number of items

The graph of the solutions of a linear inequality (in x) on a number line

See Sinusoid.

An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

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.

A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

An interval that extends to -? or ? (or both).

If ab = 0 , then either a = 0 or b = 0.