Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum
ISBN #9781119379331
7th Edition
5,101 Questions
Homework Questions
Calculus is an expansive text that builds from fundamental concepts like functions, limits, and continuity, providing a solid groundwork for all subsequent topics. It then explores the derivative through its various interpretations—ranging from instantaneous rates of change to a comprehensive toolkit of differentiation shortcuts—and applies these ideas in optimizing and modeling real-world systems. Integration is treated with equal depth, with chapters dedicated to understanding definite integrals, constructing antiderivatives, and employing diverse techniques for evaluating even the most complex integrals. The book further enriches its exploration by delving into sequences, series, function approximations, and differential equations, ultimately equipping readers with robust analytical tools essential for advanced mathematical analysis and practical applications.
Chapter 1
Foundation for Claculus: Functions and Limits
Chapter 2
Key Concept: The Derivative
Chapter 3
Short-Cuts to Differentiation
Chapter 4
Using the Derivative
Chapter 5
Key Concept: The Definite Integra
Chapter 6
Constructing Antiderivatives
Chapter 7
Integration
Chapter 8
Using the Definite Integral
Chapter 9
Sequences and Series
Chapter 10
Approximating Functions Using Series
Chapter 11
Differential Equations
Problem 1
Figure 5.11 shows the velocity of a car for $0 \leq t \leq 12$ and the rectangles used to estimate the distance traveled. (a) Do the rectangles represent a left or a right sum? (b) Do the rectangles lead to an upper or a lower estimate? (c) What is the value of $n ?$ (d) What is the value of $\Delta t ?$ (e) Give an approximate value for the estimate. (FIGURE CAN'T COPY)
Pawan Yadav Numerade Educator
Problem 2
A car accelerates at a constant rate from 44 ft/sec to 88 ft/sec in 5 seconds. (a) Figure 5.18 shows the velocity of the car while it is accelerating. What are the values of $a, b$ and $c$ in the figure? (b) How far does the car travel while it is accelerating? (FIGURE CAN'T COPY)
Lucas Finney Numerade Educator
Problem 3
Figure 5.14 shows the velocity of an object for $0 \leq t \leq$ 8. Calculate the following estimates of the distance the object travels between $t=0$ and $t=8,$ and indicate whether each is an upper or lower estimate of the distance traveled. (a) A left sum with $n=2$ subdivisions (b) A right sum with $n=2$ subdivisions (FIGURE CAN'T COPY)
Sheryl Ezze Numerade Educator
Problem 4
Figure 5.79 shows the rate, $f(x),$ in thousands of algae per hour, at which a population of algae is growing, where $x$ is in hours. (a) Estimate the average value of the rate over the interval $x=-1$ to $x=3.$ (b) Estimate the total change in the population over the interval $x=-3$ to $x=3.$ (Check your book to see figure)
Chris Trentman Numerade Educator
Problem 5
A bicyclist is pedaling along a straight road for one hour with a velocity $v$ shown in Figure $5.22 .$ She starts out five kilometers from the lake and positive velocities take her toward the lake. INote: The vertical lines on the graph are at 10 -minute ( $1 / 6$ -hour) intervals.] (a) Does the cyclist ever turn around? If so, at what time(s)? (b) When is she going the fastest? How fast is she going then? Toward the lake or away? (c) When is she closest to the lake? Approximately how close to the lake does she get? (d) When is she farthest from the lake? Approximately how far from the lake is she then? (e) What is the total distance she traveled? (GRAPH CAN'T COPY)
Adam Dehollander Numerade Educator
Problem 6
Rotate the bell-shaped curve $y=e^{-x^{2} / 2}$ shown in Figure 8.41 around the $y$ -axis, forming a hill-shaped solid of revolution. By slicing horizontally, find the volume of this hill. CAN'T COPY THE FIGURE
Carson Merrill Numerade Educator
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