Find the positive values of x for which the series > ann is convergent. n=1 o Is the function f(x) = > -nx2 xe continuous at x = 0? Explain your n=0
Find the positive values of x for which the series > ann is convergent. n=1 o Is the function f(x) = > -nx2 xe continuous at x = 0? Explain your n=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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Solve the second problem using Calc 2
![**Problem 1: Convergence of Series**
Find the positive values of \( x \) for which the series
\[
\sum_{n=1}^{\infty} x^{\ln n}
\]
is convergent.
---
**Problem 2: Continuity of Function**
Is the function
\[
f(x) = \sum_{n=0}^{\infty} x e^{-nx^2}
\]
continuous at \( x = 0 \)? Explain your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0e3b137-93c3-4f8a-ba86-2ec6c73db472%2F102d23fa-c876-41e7-bc18-704bda81d736%2Fiqhz44d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 1: Convergence of Series**
Find the positive values of \( x \) for which the series
\[
\sum_{n=1}^{\infty} x^{\ln n}
\]
is convergent.
---
**Problem 2: Continuity of Function**
Is the function
\[
f(x) = \sum_{n=0}^{\infty} x e^{-nx^2}
\]
continuous at \( x = 0 \)? Explain your reasoning.
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