Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
#93: a, b, & c
![**Chapter 3: Differentiation**
**93. Proof**
Prove each differentiation rule.
(a) \(\frac{d}{dx}[\cot x] = -\csc^2 x\)
(b) \(\frac{d}{dx}[\sec x] = \sec x \tan x\)
(c) \(\frac{d}{dx}[\csc x] = -\csc x \cot x\)
**94. Rate of Change**
Determine whether there are values of \(x\) in the interval \([0, 2\pi]\) such that the rate of change of \(f(x) = \sec x\) and the rate of change of \(g(x)\) are equal.
**95. Modeling Data**
The table shows the expenditures \(h\) (in billions of dollars) in the United States, the population \(p\) (in millions) of the United States during the years 2004 through 2009. The year is represented by \(t\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39660209-0130-4531-8e39-edad714133c0%2Fe99cf8fa-96ce-41f0-97b0-6c5c3f8452c4%2Fr5bp4z4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chapter 3: Differentiation**
**93. Proof**
Prove each differentiation rule.
(a) \(\frac{d}{dx}[\cot x] = -\csc^2 x\)
(b) \(\frac{d}{dx}[\sec x] = \sec x \tan x\)
(c) \(\frac{d}{dx}[\csc x] = -\csc x \cot x\)
**94. Rate of Change**
Determine whether there are values of \(x\) in the interval \([0, 2\pi]\) such that the rate of change of \(f(x) = \sec x\) and the rate of change of \(g(x)\) are equal.
**95. Modeling Data**
The table shows the expenditures \(h\) (in billions of dollars) in the United States, the population \(p\) (in millions) of the United States during the years 2004 through 2009. The year is represented by \(t\).
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