- 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
See Inverse tangent function.
Complex numbers a + bi and a - bi
A function that is continuous on its entire domain
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
An identity involving a trigonometric function of 2u
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.
Sum of a finite number of terms.
First-degree equation in x , y, and z
An equation that can be written in the form.
A statement that compares two quantities using an inequality symbol
Inverse tangent function
The function y = tan-1 x
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval
A triangle in which one angle is greater than 90°.
Polar form of a complex number
See Trigonometric form of a complex number.
See Power function
Real part of a complex number
See Complex number.
A logarithmic scale used in measuring the intensity of an earthquake.
A line that is neither horizontal nor vertical
Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.
A matrix consisting entirely of zeros.
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