Ron Larson, Bruce Edwards
ISBN #9780547209982
9th Edition
6,875 Questions
Homework Questions
Calculus of a Single Variable is a comprehensive textbook that introduces the key concepts of calculus using a blend of analytical, numerical, and graphical approaches. It begins by establishing essential mathematical foundations before progressing through the core topics of limits, differentiation, and integration, and further explores advanced subjects such as infinite series and differential equations. Each chapter methodically illustrates how theoretical principles are applied to solve practical problems in science and engineering, emphasizing real-world applications from modeling physical phenomena to analyzing data. Through its clear explanations, strategic progression, and numerous practical examples, the book offers a robust framework for students to master the intricacies of single-variable calculus.
Chapter 0
Preparation for Calculus
Chapter 1
Limits and Their Properties
Chapter 2
Differentiation
Chapter 3
Applications of Differentiation
Chapter 4
Integration
Chapter 5
Logarithmic, Exponential, and Other Transcendental Functions
Chapter 6
Differential Equations
Chapter 7
Applications of Integration
Chapter 8
Integration Techniques, L’Hopital’s Rule, and Improper Integrals
Chapter 9
Infinite Series
Chapter 10
Conics, Parametric Equations, and Polar Coordinates
Problem 1
Find two positive numbers whose sum is 110 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) (b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.) (c) Write the product $P$ as a function of $x$. (d) Use a graphing utility to graph the function in part (c) and estimate the solution from the graph. (e) Use calculus to find the critical number of the function in part (c). Then find the two numbers.
Angelos Evangelinos Numerade Educator
Problem 2
In Exercises $1-6,$ find the value of the derivative (if it exists) at each indicated extremum. $$ f(x)=\frac{x^{2}}{x^{2}+4} $$
Linh Vu Numerade Educator
Problem 3
In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function. $$ \begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array} $$ Graph cannot copy.
Christopher Mark Numerade Educator
Problem 4
Match the graph of $f$ in the left column with that of its derivative in the right column.
Alejandro Marquez Numerade Educator
Problem 5
Use Example 1 as a model to evaluate the limit $\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(c_{i}\right) \Delta x_{i}$ over the region bounded by the graphs of the equations. $f(x)=\sqrt{x}, \quad y=0, \quad x=0, \quad x=3$ (Hint: Let $c_{i}=3 i^{2} / n^{2} . )$
Problem 6
Assume that $x$ and $y$ are both differentiable functions of $t$ and find the required values of $d y / d t$ and $d x / d t .$ Equation $\quad$ Find $\quad$ Given $\begin{array}{rlrl}{y=\sqrt{x}} & {\text { (a) } \frac{d y}{d t} \text { when } x=4} & {} & {\frac{d x}{d t}=3} \\ {} & {\text { (b) } \frac{d x}{d t} \text { when } x=25} & {} & {\frac{d y}{d t}=2}\end{array}$
Caleb Fink Numerade Educator
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