Ross L. Finney, Franklin D. Demana, Bet K. Waits, Daniel Kennedy
ISBN #9780132014083
3rd Edition
2,343 Questions
Homework Questions
Calculus: Graphical, Numerical, Algebraic is a comprehensive exploration of fundamental calculus concepts, blending rigorous theory with real-world applications. The book begins by establishing essential prerequisites like exponential functions and limits, laying the groundwork for understanding dynamic systems and modeling phenomena such as radioactive decay and market behaviors. It then delves into the intricacies of derivatives, integrals, and differential equations, illustrating how these tools can solve practical problems in engineering, economics, and the natural sciences. Throughout, the text emphasizes the interconnectedness of graphical, numerical, and algebraic approaches, equipping readers with versatile strategies for tackling both theoretical challenges and applied situations.
Chapter 1
Prerequisites for Calculus
Chapter 2
Limits and Continuity
Chapter 3
Derivatives
Chapter 4
Applications of Derivatives
Chapter 5
The Definite Integral
Chapter 6
Differential Equations and Mathematical Modeling
Chapter 7
Applications of Definite Integrals
Problem 1
In Exercises $1-6,$ (a) find the linearization $L(x)$ of $f(x)$ at $x=a$ . (b) How accurate is the approximation $L(a+0.1) \approx f(a+0.1) ?$ See the comparisons following Example $1 .$ $f(x)=x^{3}-2 x+3, \quad a=2$
Oswaldo Jiménez Numerade Educator
Problem 2
(a) Write the volume $V$ of a cube as a function of the side length $s$ . (b) Find the (instantaneous) rate of change of the volume V with respect to a side s. (c) Evaluate the rate of change of $V$ at $s=1$ and $s=5$ (d) If $s$ is measured in inches and $V$ is measured in cubic inches, what units would be appropriate for $d V / d s ?$
Mutahar Mehkri Numerade Educator
Problem 3
In Exercises $1-6,$ find the average rate of change of the function over each interval. $f(x)=x^{3}+1$ (a) $$[2,3] \quad$$ $(b)\lceil- 1,1]$
Bahar Tehranipoor Numerade Educator
Problem 4
In Exercises 1-4, use the definition $f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$ to find the derivative of the given function at the indicated point. $f(x)=1 / x, a=2$
Problem 5
In Exercises $1-8,$ use graphs and tables to find (a) $\lim _{x \rightarrow \infty} f(x)$ and (b) $\lim _{x \rightarrow-\infty} f(x)$ (c) Identify all horizontal asymptotes. $$f(x)=\cos \left(\frac{1}{x}\right)$$
Foster Wisusik Numerade Educator
Problem 6
A particle starts at $x=0$ and moves along the $x$ -axis with velocity $v(t)=5$ for time $t \geq 0$ . Where is the particle at $t=4$ ?
Xiaomeng Zhang Numerade Educator
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