Set g(x)= Question 1 g'(0) = = y = arctan(x)f(x). Suppose f(0) = 5 and lim h→0 f(0 + h) - f(0) h = 3 Exact answers must be provided and expressions involving arctan (0) must be converted to radian measure. π π ㅠ π For example, arctan (√3) = since is the angle between (F) √√3. 3 3 2 2 Question 2 The equation of the tangent line of g at 0 is and such that tan =
Set g(x)= Question 1 g'(0) = = y = arctan(x)f(x). Suppose f(0) = 5 and lim h→0 f(0 + h) - f(0) h = 3 Exact answers must be provided and expressions involving arctan (0) must be converted to radian measure. π π ㅠ π For example, arctan (√3) = since is the angle between (F) √√3. 3 3 2 2 Question 2 The equation of the tangent line of g at 0 is and such that tan =
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
![Set \( g(x) = \arctan(x)f(x) \). Suppose \( f(0) = 5 \) and
\[
\lim_{h \to 0} \frac{f(0 + h) - f(0)}{h} = 3
\]
**Question 1**
\( g'(0) = \)
(Exact answers must be provided and expressions involving \(\arctan(0)\) must be converted to radian measure. For example, \(\arctan(\sqrt{3}) = \frac{\pi}{3}\) since \(\frac{\pi}{3}\) is the angle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) such that \(\tan\left(\frac{\pi}{3}\right) = \sqrt{3}\).)
**Question 2**
The equation of the tangent line of \( g \) at 0 is
\( y = \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9913a63-42b8-4d7b-b639-ea44a4bc708b%2F54a6a0a2-5910-4448-9a14-1a90c4b91a74%2Fqjgu428_processed.png&w=3840&q=75)
Transcribed Image Text:Set \( g(x) = \arctan(x)f(x) \). Suppose \( f(0) = 5 \) and
\[
\lim_{h \to 0} \frac{f(0 + h) - f(0)}{h} = 3
\]
**Question 1**
\( g'(0) = \)
(Exact answers must be provided and expressions involving \(\arctan(0)\) must be converted to radian measure. For example, \(\arctan(\sqrt{3}) = \frac{\pi}{3}\) since \(\frac{\pi}{3}\) is the angle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) such that \(\tan\left(\frac{\pi}{3}\right) = \sqrt{3}\).)
**Question 2**
The equation of the tangent line of \( g \) at 0 is
\( y = \)
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