Using the definition of continuity and the example below(method for solving the question), show that the following function is continuous q(z) = 1/z^3 at z0 ∈ (0, ∞).
Using the definition of continuity and the example below(method for solving the question), show that the following function is continuous q(z) = 1/z^3 at z0 ∈ (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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Question
Using the definition of continuity and the example below(method for solving the question), show that the following function is continuous q(z) = 1/z^3 at z0 ∈ (0, ∞).

Transcribed Image Text:Example Consider f(x) = 1 1/2 2²1 defined on
Show Hx) is continuous at any at Ri{o}
| f(x) = fl(a)| = | -=-=2 = = = = 2 | = |
Consider
A:
ㅎ
0/2
fa-alla+al
x²²a²
STEP 1 Let a>o. Suppose we
a
=
Ix-all [xx+a)=
22a7
HE
T.e. 12-α| < ²/1/20
39/21 So í Tal < 24₁ < 31a|
i
i
2
TV
a²-a²
x²a²
2
lal
PR\203
1
we need to bound
this
consider x = (2, 30)
8=%2.
1.2.
↓
1x1 <31a1
2
⇓
-
Betal ≤1x1+lal < 5lat
2.

Transcribed Image Text:STEP 2
215/al!
3
1191²
so
[f(c)-flall <loxc-ali
1/1/2-1/²
= |x-a)=1/135810201²3
lal
la).
which is less than & if
8 < 2 191³
10
chorse S= min { lai, slap²³ }
10
to accommodate Stept and stop 2
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