Larry J. Goldstein, David C. Lay, David I. Schneider
ISBN #9780134437774
14th Edition
3,033 Questions
Homework Questions
Calculus and Its Applications introduces readers to the fundamental principles of calculus by starting with basic functions and progressively exploring derivatives, integration, and differential equations. The book builds a strong analytical foundation through detailed explanations of key concepts such as the power and chain rules, techniques of differentiation, and methods of integration. It seamlessly weaves theory with practical applications, demonstrating how calculus aids in solving real-world problems in physics, economics, engineering, and beyond. Additionally, the text expands its scope to cover multivariable functions, optimization problems, and the interplay between calculus and probability, equipping students with versatile tools for advanced mathematical analysis.
Chapter 0
Functions
Chapter 1
The Derivative
Chapter 2
Applications of the Derivative
Chapter 3
Techniques of Differentiation
Chapter 4
The Exponential and Natural Logarithm Functions
Chapter 5
Applications of the Exponential and Natural
Chapter 6
The Definite Integral
Chapter 7
Functions of Several Variables
Chapter 8
The Trigonometric Functions
Chapter 9
Techniques of Integration
Chapter 10
Differential Equations
Chapter 11
Taylor Polynomials and Infinite Series
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Chapter 12
Probability and Calculus
Problem 1
Find the logarithmic derivative and then determine the percentage rate of change of the functions at the points indicated. $$f(t)=t^{2} \text { at } t=10 \text { and } t=50$$
Linh Vu Numerade Educator
Problem 2
Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). $$f(x)=\frac{1}{18} x, 0 \leq x \leq 6$$
Sriram Soundarrajan Numerade Educator
Problem 3
Draw the following intervals on the number line. $$[-1,4]$$
Willis James Numerade Educator
Problem 4
Find the slopes and $y$-intercepts of the following lines. $$y=3-7 x$$
Problem 5
Determine the growth constant $k$, then find all solutions of the given differential equation. $$y^{\prime}=y$$
Joseph Liao Numerade Educator
Problem 6
Refer to the functions whose graphs are given in Fig. 17. Which functions have a positive first derivative for all $x ?$
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