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
Please help me with how to do part b
![**2. Estimate the following:**
**(a)**
\[ \sin(3.14) \rightarrow \sin(x) \]
Let \( z = \pi \) and \( x = 3.14 \).
\[ f(x) = \sin x \rightarrow f(z) = f(\pi) = \sin \pi = 0 \]
\[ f'(x) = \cos x \rightarrow f'(z) = f'(\pi) = \cos \pi = -1 \]
\[ L(x) = 0 + (-1)(x - \pi) = -(x - \pi) = \pi - x \]
\[ L(3.14) = \pi - 3.14 \]
**(b)**
\[ \frac{1}{(0.99)^2} \]
This section appears to involve estimating or simplifying mathematical expressions using linear approximations or derivative-based methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb234898a-ca00-4740-ae3d-79576f672843%2Fad50abc9-bd9d-46e3-a36b-11626e4da0d1%2Fqs5mgh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**2. Estimate the following:**
**(a)**
\[ \sin(3.14) \rightarrow \sin(x) \]
Let \( z = \pi \) and \( x = 3.14 \).
\[ f(x) = \sin x \rightarrow f(z) = f(\pi) = \sin \pi = 0 \]
\[ f'(x) = \cos x \rightarrow f'(z) = f'(\pi) = \cos \pi = -1 \]
\[ L(x) = 0 + (-1)(x - \pi) = -(x - \pi) = \pi - x \]
\[ L(3.14) = \pi - 3.14 \]
**(b)**
\[ \frac{1}{(0.99)^2} \]
This section appears to involve estimating or simplifying mathematical expressions using linear approximations or derivative-based methods.
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