Determine where f'(x) exists, an expression for it, and where f'(x) is con- tinuous: f(z) = { 0 atsin(금) ;2 +0 ;x = 0
Determine where f'(x) exists, an expression for it, and where f'(x) is con- tinuous: f(z) = { 0 atsin(금) ;2 +0 ;x = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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COURSE: Mathematical Analysis/
TOPIC: Differentiation
![**Problem Statement:**
Determine where \( f'(x) \) exists, an expression for it, and where \( f'(x) \) is continuous:
\[
f(x) =
\begin{cases}
x^4 \sin\left(\frac{1}{x^2}\right) & ; x \neq 0 \\
0 & ; x = 0
\end{cases}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2Fc2915d82-3b90-42dd-bf0c-b84f280c45e6%2Fu27jh5o_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine where \( f'(x) \) exists, an expression for it, and where \( f'(x) \) is continuous:
\[
f(x) =
\begin{cases}
x^4 \sin\left(\frac{1}{x^2}\right) & ; x \neq 0 \\
0 & ; x = 0
\end{cases}
\]
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