Joel Hass, Maurice D. Weir, George B. Thomas, Jr.
ISBN #9780321999580
3rd Edition
6,517 Questions
Homework Questions
University Calculus: Early Transcendentals is a comprehensive textbook that systematically builds the fundamentals of calculus, starting with functions and limits before progressing to derivatives, integrals, and their many applications. The book guides readers through a natural development of topics—from the pioneering ideas of switching between representations of functions to the advanced techniques of multivariable calculus and vector analysis. Emphasizing both theory and practice, it connects abstract mathematical ideas to real-world challenges in science, engineering, and economics. Overall, the text serves as an indispensable resource for students aiming to master the versatile tools of calculus while applying them to diverse problems.
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
Integrals and Transcendental Functions
Chapter 8
Techniques of Integration
Chapter 9
Infinite Sequences and Series
Chapter 10
Parametric Equations and Polar Coordinates
Chapter 11
Vectors and the Geometry of Space
Chapter 12
Vector-Valued Functions and Motion in Space
View More
Chapter 13
Partial Derivatives
Chapter 14
Multiple Integrals
Chapter 15
Integrals and Vector Fields
Problem 1
Sketch the interval $(a, b)$ on the $x$ -axis with the point $c$ inside. Then find a value of $\delta>0$ such that for all $x, 0<|x-c|<\delta \Rightarrow a<x<b$ $$a=1, \quad b=7, \quad c=5$$
Lucas Finney Numerade Educator
Problem 2
Using integration by parts. $$\int x \sin \frac{x}{2} d x$$
Kian Manafi Numerade Educator
Problem 3
Use the grid and a straight edge to make a rough estimate of the slope of the curve (in $y$ -units per $x$ -unit) at the points $P_{1}$ and $P_{2}$. (GRAPH CAN'T COPY)
Christy Galilei Numerade Educator
Problem 4
Each exercise gives a formula for the $n$ th term $a_{n}$ of a sequence $\left\{a_{n}\right\} .$ Find the values of $a_{1}, a_{2}, a_{3},$ and $a_{4}$. $$a_{n}=\frac{1-n}{n^{2}}$$
Nick Johnson Numerade Educator
Problem 5
Find the points on the ellipse $x^{2}+2 y^{2}=1$ where $f(x, y)=x y$ has its extreme values.
Problem 6
Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises $1-46$. a. $\int_{0}^{3} \sqrt{y+1} d y$ b. $\int_{-1}^{0} \sqrt{y+1} d y$
Gregory Higby Numerade Educator
WHAT OUR STUDENTS SAY
“I finally understand my textbook questions. Before Numerade, I’d skip hard problems. Now I get instant help with videos that explain everything simply.”
Edwin V. Penn State Freshman