- 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
Addition property of equality
If u = v and w = z , then u + w = v + z
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
Reciprocal of the period of a sinusoid.
Inverse sine function
The function y = sin-1 x
Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0
A procedure for fitting a logistic curve to a set of data
Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)
Negative linear correlation
See Linear correlation.
See Additive inverse of a real number and Additive inverse of a complex number.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
The distance from the center to a vertex of an ellipse.
See Finite sequence, Infinite sequence.
Trigonometric form of a complex number
r(cos ? + i sin ?)
Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.
A letter that represents an unspecified number.
Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.
A point that lies on both the graph and the y-axis.