3. For a, b>0 define f(x) by f(x) = Tot tz ta dt log blog a Prove or disprove that f is continuous at x = -1. x = -1 x = -1.
3. For a, b>0 define f(x) by f(x) = Tot tz ta dt log blog a Prove or disprove that f is continuous at x = -1. x = -1 x = -1.
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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![3. For \( a, b > 0 \) define \( f(x) \) by
\[
f(x) =
\begin{cases}
\int_{a}^{b} t^x \, dt & x \neq -1 \\
\log b - \log a & x = -1
\end{cases}
\]
Prove or disprove that \( f \) is continuous at \( x = -1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabba7d05-e030-4d49-ac3b-b588659cd1ab%2F23114597-e0dd-4d3e-a1bd-608203938f3c%2F6is2di5_processed.png&w=3840&q=75)
Transcribed Image Text:3. For \( a, b > 0 \) define \( f(x) \) by
\[
f(x) =
\begin{cases}
\int_{a}^{b} t^x \, dt & x \neq -1 \\
\log b - \log a & x = -1
\end{cases}
\]
Prove or disprove that \( f \) is continuous at \( x = -1 \).
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