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George B. Thomas, Jr.
ISBN #9780321878960
13th Edition
6,812 Questions
Homework Questions
Thomas Calculus is a comprehensive guide to both single-variable and multivariable calculus that builds a deep understanding of mathematical principles through clear explanations and real-world applications. The text methodically covers foundational topics such as functions, limits, derivatives, and integrals, before progressing to advanced subjects like transcendental functions, vector calculus, and partial derivatives. Each section emphasizes rigorous analysis and problem-solving techniques, integrating practical examples from physics, engineering, and economics. Overall, the book equips students with essential tools to model and solve complex problems while fostering a solid conceptual grasp of calculus.
Chapter 1
Functions
Chapter 2
Limits and Continuity
Chapter 3
Derivatives
Chapter 4
Applications of Derivatives
Chapter 5
Integrals
Chapter 6
Applications of Definite Integrals
Chapter 7
Transcendental Functions
Chapter 8
Techniques of Integration
Chapter 9
First-Order Differential Equations
Chapter 10
Infinite Sequences and Series
Chapter 11
Parametric Equations and Polar Coordinates
Chapter 12
Vectors and the Geometry of Space
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Chapter 13
Vector-Valued Functions and Motion in Space
Chapter 14
Partial Derivatives
Chapter 15
Multiple Integrals
Chapter 16
Integrals and Vector Fields
Problem 1
In Exercises $1-6,$ find the domain and range of each function. $$f(x)=1+x^{2}$$
Mengchun Cai Numerade Educator
Problem 2
In Exercises $1-6,$ find the domain and range of each function. $$f(x)=1-\sqrt{x}$$
Willis James Numerade Educator
Problem 3
Find the average rate of change of the function over the given interval or intervals. $f(x)=x^{3}+1$ a. $[2,3] \quad$ b. $[-1,1]$
Tyler Fyock Numerade Educator
Problem 4
The solid lies between planes perpendicular to the $x$ -axis at $x=0$ and $x=4 .$ The cross-sections perpendicular to the axis on the interval $0 \leq x \leq 4$ are squares whose diagonals run from the parabola $y=-\sqrt{x}$ to the parabola $y=\sqrt{x}$ .
Hossam Mohamed Numerade Educator
Problem 5
For the function $g(x)$ graphed here, find the following limits or explain why they do not exist. \begin{equation} \text { a. }\lim _{x \rightarrow 1} g(x) \quad \text { b. } \lim _{x \rightarrow 2} g(x) \quad \text { c. } \lim _{x \rightarrow 3} g(x) \quad \text { d. } \lim _{x \rightarrow 2.5} g(x) \end{equation}
Melissa Munoz Numerade Educator
Problem 6
In Exercises $1-16,$ give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$x=2, \quad y=3$$
Elizabeth Xu Numerade Educator
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