Ron Larson, Bruce Edwards
ISBN #9781285060286
10th Edition
6,214 Questions
Homework Questions
Calculus of a Single Variable is a meticulously structured textbook that builds a deep understanding of both fundamental and advanced calculus concepts through a progressive, step-by-step approach. It starts by establishing essential pre-calculus skills before delving into core topics like limits, differentiation, and integration, and further explores applications that bridge theory with real-world problems in physics, engineering, and beyond. The book methodically introduces advanced techniques, including the study of transcendental functions, differential equations, and infinite series, while also integrating geometric perspectives with conics, parametric equations, and polar coordinates. Emphasizing a blend of analytical, numerical, and graphical methods, this text equips students with the versatile problem-solving tools necessary for mastering calculus and its extensive applications.
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
Finding $u$ and $d u$ In Exercises $1-4,$ complete the table by identifying $u$ and $d u$ for the integral. $$ \begin{array}{l}{\int f(g(x)) g^{\prime}(x) d x \quad u=g(x) \quad d u=g^{\prime}(x) d x} \\ {\int\left(8 x^{2}+1\right)^{2}(16 x) d x}\end{array} $$
Dwijendra Rao Numerade Educator
Problem 2
Evaluating a Function In Exercises $1-10$ , evaluate the function at the given value(s) of the independent variable. Simplify the results. $$ \begin{array}{l}{f(x)=7 x-4} \\ {\text { (a) } f(0) \quad \text { (b) } f(-3)} \\ {\text { (c) } f(b) \quad \text { (d) } f(x-1)}\end{array} $$
Narayan Hari Numerade Educator
Problem 3
Precalculus or Calculus In Exercises $1-5,$ decide whether the problem can be solved using precalculus or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical approach to estimate the solution. Find the distance traveled in 15 seconds by an object traveling at a constant velocity of 20 feet per second.
Oswaldo Jiménez Numerade Educator
Problem 4
Numerical, Graphical, and Analytic Analysis 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.) $$ \begin{array}{|c|c|c|}\hline \text { First } & {\text { Second }} \\ {\text { Number, } x} & {\text { Number }} & {\text { Product, } P} \\ \hline 10 & {110-10} & {10(110-10)=1000} \\ \hline 20 & {110-20} & {20(110-20)=1800} \\ \hline\end{array} $$ (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.
Paul Choe Numerade Educator
Problem 5
Matching In Exercises $1-4,$ match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).] $$ y=-\frac{3}{2} x+3 $$
Carson Merrill Numerade Educator
Problem 6
In Exercises 1–6, evaluate the function. If the value is not a rational number, round your answer to three decimal places. $$ \begin{array}{l}{\text { (a) } \sinh 3} \\ {\text { (b) } \tanh (-2)}\end{array} $$
Anurag Kumar Numerade Educator
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