Question

**If you use handwritten, please provide clear hand
written**

Compact and analysis conception

1. Are all closed interval compact?

for example [0,1]. are they closed and bounded?

2. If i can find the Maximum and Minimum, does that mean the set is closed and bounded?

Answer #1

If you use handwritten, please provide clear hand
written
Compact and analysis conception
1. Are all closed interval compact? For example
[0,1]. are they closed and bounded?
2. If i can find the Maximum and Minimum, does that mean the set
is closed and bounded?

Show all the steps and explain. Don't skip steps and please
clear hand written
f(x)=x^m sin(1/x^n) if
x is not equal 0 and f(x)=0 if x =0
(a) prove that when
m>1+n, then the derivative of f is continuous at 0
limit x to 0 x^n
sin(1/x^n) does not exist? but why??? please explain it should be
0*sin(1/x^n)

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24
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