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3. Let [x] be the greatest integer less than or equal to z. So [2.7) = 2, L-3.4] =-4, and [3] = 3. Let f(x) = [sin(x)] and g(x)=x[r]. a. Is f continuous at x = π/2? Justify! b. Is f continuous at x = 3/2? Justify! c. Is g continuous at x = 0? Justify!

3. Let [x] be the greatest integer less than or equal to z. So [2.7) = 2, L-3.4] =-4, and [3] = 3. Let f(x) = [sin(x)] and g(x)=x[r]. a. Is f continuous at x = π/2? Justify! b. Is f continuous at x = 3/2? Justify! c. Is g continuous at x = 0? Justify!

Advanced Engineering Mathematics
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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Certainly! Below is the transcription suitable for an educational website: --- 3. Let \(\lfloor x \rfloor\) be the greatest integer less than or equal to \(x\). So \(\lfloor 2.7 \rfloor = 2\), \(\lfloor -3.4 \rfloor = -4\), and \(\lfloor 3 \rfloor = 3\). Let \( f(x) = |\sin(x)| \) and \( g(x) = x \lfloor x \rfloor \). a. Is \( f \) continuous at \( x = \pi/2 \)? Justify! b. Is \( f \) continuous at \( x = 3\pi/2 \)? Justify! c. Is \( g \) continuous at \( x = 0 \)? Justify! --- Please provide any details on illustrations or graphs if there are any, otherwise this transcription conveys the necessary information.
Transcribed Image Text:Certainly! Below is the transcription suitable for an educational website: --- 3. Let \(\lfloor x \rfloor\) be the greatest integer less than or equal to \(x\). So \(\lfloor 2.7 \rfloor = 2\), \(\lfloor -3.4 \rfloor = -4\), and \(\lfloor 3 \rfloor = 3\). Let \( f(x) = |\sin(x)| \) and \( g(x) = x \lfloor x \rfloor \). a. Is \( f \) continuous at \( x = \pi/2 \)? Justify! b. Is \( f \) continuous at \( x = 3\pi/2 \)? Justify! c. Is \( g \) continuous at \( x = 0 \)? Justify! --- Please provide any details on illustrations or graphs if there are any, otherwise this transcription conveys the necessary information.
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