(4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10 ifz¢ Z. Prove that for any a e R, we have lim f(x) = 0.
(4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10 ifz¢ Z. Prove that for any a e R, we have lim f(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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![(4) Let \( f(x) \) be the function whose domain is all of \(\mathbb{R}\) given by the rule
\[
f(x) =
\begin{cases}
42 & \text{if } x \in \mathbb{Z} \text{ and} \\
0 & \text{if } x \notin \mathbb{Z}.
\end{cases}
\]
Prove that for any \( a \in \mathbb{R} \), we have \(\lim_{x \to a} f(x) = 0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba5a3306-2973-4825-a0c7-f3a4b662c857%2F146fb964-0f26-4a15-a7e6-d13a24cb53ce%2Fe2uzsya_processed.png&w=3840&q=75)
Transcribed Image Text:(4) Let \( f(x) \) be the function whose domain is all of \(\mathbb{R}\) given by the rule
\[
f(x) =
\begin{cases}
42 & \text{if } x \in \mathbb{Z} \text{ and} \\
0 & \text{if } x \notin \mathbb{Z}.
\end{cases}
\]
Prove that for any \( a \in \mathbb{R} \), we have \(\lim_{x \to a} f(x) = 0\).
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