William Briggs, Lyle Cochran, Bernard Gillet
ISBN #9780134763644
3rd Edition
8,978 Questions
Homework Questions
Calculus: Early Transcendentals is a comprehensive textbook that gradually builds the foundation of calculus from fundamental functions to advanced concepts in multivariable and vector analysis. It begins by establishing the language of functions, limits, and derivatives, then methodically advances through integration, series, and differential equations, setting the stage for more intricate applications. The text features a progression of techniques—from Riemann sums and the Fundamental Theorem of Calculus to Lagrange multipliers and divergence and curl—all illustrated with real-world applications in physics, engineering, and economics. By seamlessly integrating theoretical rigor with practical problem-solving, the book serves as both a vital learning tool and a valuable reference for students and professionals pursuing deeper mastery of calculus.
Chapter 1
Functions
Chapter 2
Limits
Chapter 3
Derivatives
Chapter 4
Applications of the Derivative
Chapter 5
Integration
Chapter 6
Applications of Integration
Chapter 7
Logarithmic, Exponential. and Hyperbolic Functions
Chapter 8
Integration Techniques
Chapter 9
Differential Equations
Chapter 10
Sequences and Infinite Series
Chapter 11
Power Series
Chapter 12
Parametric and Polar Curves
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Chapter 13
Vectors and the Geometry of Space
Chapter 14
Vector-Valued Functions
Chapter 15
Functions of Several Variables
Chapter 16
Multiple Integration
Chapter 17
Vector Calculus
Problem 1
Set up a sum of two integrals that equals the area of the shaded region bounded by the graphs of the functions $f$ and $g$ on $[a, c]$ (see figure). Assume the curves intersect at $x=b$.
Taylor Francis Numerade Educator
Problem 2
Suppose an object moves along a line at $15 \mathrm{m} / \mathrm{s},$ for $0 \leq t<2$ and at $25 \mathrm{m} / \mathrm{s},$ for $2 \leq t \leq 5,$ where $t$ is measured in seconds. Sketch the graph of the velocity function and find the displacement of the object for $0 \leq t \leq 5$.
Jacob Steele Numerade Educator
Problem 3
Why is it not possible to evaluate $\lim _{x \rightarrow 0} \frac{\sin x}{x}$ by direct substitution?
Sanchit Jain Numerade Educator
Problem 4
Explain the meaning of $\lim _{x \rightarrow-\infty} f(x)=10$.
Cinsy Krehbiel Numerade Educator
Problem 5
Plot the points with polar coordinates $(2, \pi / 6)$ and $(-3,-\pi / 2)$ Give two alternative sets of coordinate pairs for both points.
Jason Orozco Numerade Educator
Problem 6
Explain how the first derivative of a function determines where the function is increasing or decreasing.
Abdul Ibitoye Numerade Educator
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