Book cover for University Calculus: Early Transcendentals

University Calculus: Early Transcendentals

Joel Hass, Maurice D. Weir, George B. Thomas, Jr.

ISBN #9780321999580

3rd Edition

6,517 Questions

Group icon
42,715 Students Helped

Homework Questions

Right arrow

Summary

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.

Chapters & Topics Covered

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

Popular Video Solutions

Play button

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

Lucas Finney   Numerade Educator

Play button

Problem 2

Using integration by parts. $$\int x \sin \frac{x}{2} d x$$

Kian Manafi

Kian Manafi   Numerade Educator

Play button

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

Christy Galilei   Numerade Educator

Play button

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

Nick Johnson   Numerade Educator

Play button

Problem 5

Find the points on the ellipse $x^{2}+2 y^{2}=1$ where $f(x, y)=x y$ has its extreme values.

Lucas Finney

Lucas Finney   Numerade Educator

Play button

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

Gregory Higby   Numerade Educator

Student Testimonials

‘

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

Student Student Student Student Student