Solutions for Chapter 3: Differentiation

Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

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

Variable representing the range value of a function (usually y)

The distance between real numbers a and b, or |a - b|

a b = aa 1 b b, b Z 0

Reciprocal of the period of a sinusoid.

Events A and B such that P(A and B) = P(A)P(B)

The number of degrees or radians in an angle

See Numerical derivative of ƒ at x = a.

Two vectors u and v with u x v = 0.

The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

See Multiplicative inverse of a real number.

Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

p = ƒ(x), where x represents production and p represents price

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

See Weighted mean.

The y-value of the bottom of the viewing window.