- Chapter 1: Functions
- Chapter 10: Infinite Sequences and Series
- Chapter 11: Parametric Equations and Polar Coordinates
- Chapter 12: Vectors and the Geometry of Space
- Chapter 13: Vector-Valued Functions and Motion in Space
- Chapter 14: Partial Derivatives
- Chapter 15: Multiple Integrals
- Chapter 16: Integration in Vector Fields
- Chapter 2: Limits and Continuity
- Chapter 3: Differentiation
- Chapter 4: Applications of Derivatives
- Chapter 5: Integration
- Chapter 6: Applications of Definite Integrals
- Chapter 7: Transcendental Functions
- Chapter 8: Techniques of Integration
- Chapter 9: First-Order Differential Equations
Thomas' Calculus 12th Edition - Solutions by Chapter
Full solutions for Thomas' Calculus | 12th Edition
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
See Inverse cotangent function.
An observational study that gathers data from an entire population
Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
The function y = cot x
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant
Any solution of the resulting equation that is not a solution of the original equation.
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.
The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b
Magnitude of a real number
See Absolute value of a real number
One-to-one rule of logarithms
x = y if and only if logb x = logb y.
Order of an m x n matrix
The order of an m x n matrix is m x n.
Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
Present value of an annuity T
he net amount of your money put into an annuity.
Principle of mathematical induction
A principle related to mathematical induction.
Product of functions
(ƒg)(x) = ƒ(x)g(x)
Resolving a vector
Finding the horizontal and vertical components of a vector.
Usually the third dimension in Cartesian space.