Determine the values of a where the function f (x) is not continuous. Label each discontinuity as removable f(x) = [//√x + 2x≤ 2 x+1 x>2 Enter your answers as integers in increasing order. If there are no discontinuities, enter NA in both response a
Determine the values of a where the function f (x) is not continuous. Label each discontinuity as removable f(x) = [//√x + 2x≤ 2 x+1 x>2 Enter your answers as integers in increasing order. If there are no discontinuities, enter NA in both response a
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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![**Determine the values of \( x \) where the function \( f(x) \) is not continuous. Label each discontinuity as removable, jump, or infinite.**
The function \( f(x) \) is given as:
\[
f(x) = \begin{cases}
\frac{1}{2}x + 2 & x \leq 2 \\
x + 1 & x > 2
\end{cases}
\]
**Instructions:**
- Enter your answers as integers in increasing order.
- If there are no discontinuities, enter NA in both response areas and choose continuous in both drop-down menus.
- If there is only one discontinuity, enter NA in the second response area and choose continuous in the second drop-down menu.
**Responses:**
\( x = 3 \) [continuous]
\( x = 2 \) [Click for List]
**Explanation Prompt:**
Show work and explain, in your own words, how you arrived at your answers. Answers with no relevant explanation may receive reduced or no credit.
**Note:**
The text box allows you to type your explanation with formatting options such as bold, italics, and equations, and adjust the styles, fonts, and size for emphasis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5a78c13-da5a-4255-8b88-63fe3a182f48%2F54631ff8-b277-4a0c-9dfc-2aef4635a086%2Fu5r7z8t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine the values of \( x \) where the function \( f(x) \) is not continuous. Label each discontinuity as removable, jump, or infinite.**
The function \( f(x) \) is given as:
\[
f(x) = \begin{cases}
\frac{1}{2}x + 2 & x \leq 2 \\
x + 1 & x > 2
\end{cases}
\]
**Instructions:**
- Enter your answers as integers in increasing order.
- If there are no discontinuities, enter NA in both response areas and choose continuous in both drop-down menus.
- If there is only one discontinuity, enter NA in the second response area and choose continuous in the second drop-down menu.
**Responses:**
\( x = 3 \) [continuous]
\( x = 2 \) [Click for List]
**Explanation Prompt:**
Show work and explain, in your own words, how you arrived at your answers. Answers with no relevant explanation may receive reduced or no credit.
**Note:**
The text box allows you to type your explanation with formatting options such as bold, italics, and equations, and adjust the styles, fonts, and size for emphasis.
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