Determine whether f'(0) exists, where f(x) = x² sin 0 X if x #0 if x = 0

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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Determine whether f'(0) exists, where
f(x) =
1
{ 2² sin }
if x # 0
if x = 0
Professional Writing Focus:
As always, refer to the "Professional Problem Information” handout to create a professionally
written solution. This week, you should especially focus on:
Methods: Carefully use the limit definition of f'(0). You do not need to find the derivative
at any other points.
Mathematical Details: If a ≤ b, is ax ≤ bx always true? There are several other details in
this problem - pay close attention!
Computations: Do not compute a limit by sketching a picture of the graph (or giving a
table). When possible, we must compute limits algebraically. A figure should only be included
if it illustrates a calculation you have already made.
Transcribed Image Text:Determine whether f'(0) exists, where f(x) = 1 { 2² sin } if x # 0 if x = 0 Professional Writing Focus: As always, refer to the "Professional Problem Information” handout to create a professionally written solution. This week, you should especially focus on: Methods: Carefully use the limit definition of f'(0). You do not need to find the derivative at any other points. Mathematical Details: If a ≤ b, is ax ≤ bx always true? There are several other details in this problem - pay close attention! Computations: Do not compute a limit by sketching a picture of the graph (or giving a table). When possible, we must compute limits algebraically. A figure should only be included if it illustrates a calculation you have already made.
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