Using epsilo-delta definition, prove that the 4x2 | 2x²+1 J æ=1 is 2. limit of

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Answer the following.
1. Using epsilo-delta definition, prove that the
4x2
2x2 +1 ) x=1 is 2.
limit of
2. Using the properties of convergent sequences,
S n?
-sin
2n+1
find the limit of
n=1
3. Determine if the following sequences {"n} are
increasing, decreasing, or not monotonic, and
show your proof. Also, determine an upper or
lower bound, if it exists.
An
1.
2n+1
An
2.
п
(-1)"+1
An
3.
1–2n2
an
4.
n2
n!
An
5.
3n
Transcribed Image Text:Answer the following. 1. Using epsilo-delta definition, prove that the 4x2 2x2 +1 ) x=1 is 2. limit of 2. Using the properties of convergent sequences, S n? -sin 2n+1 find the limit of n=1 3. Determine if the following sequences {"n} are increasing, decreasing, or not monotonic, and show your proof. Also, determine an upper or lower bound, if it exists. An 1. 2n+1 An 2. п (-1)"+1 An 3. 1–2n2 an 4. n2 n! An 5. 3n
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