Introduction to Real Analysis 3rd Edition - Solutions by Chapter

The opposite of b , or -b

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

An arrangement of elements of a set, in which order is not important

a + b = b + a ab = ba

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

A vector in the direction of a line in three-dimensional space

A line used to determine the conic

A set with no elements

Writing a polynomial as a product of two or more polynomial factors.

Ax + By + C = 0, where A and B are not both zero.

The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

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

a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C

A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

The function ƒ(x) = 1x

A graph of a polar equation or r = a cos nu.

An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

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