Homework Statement
The question is asking to use the ε, δ-definition of limit to show that lim x->a 1/x=1/a
Homework Equations
\lim_{x \to a} f(x) = L
The Attempt at a Solution
Here is what I have so far:
|1/x-x/a|<ε
and |x-a|<δ
I have no idea what to do...
the original question is :"use the ε, δ-definition of limit to show that lim x->a x^5=a^5
there is no actual number in it, that's why I'm stuck when I was solving the problem
I have a question about the (ε, δ)-definition of limit
lim x->a x^5=a^5
I know that |x^5-a^5|<ε
and |x-a|<δ
I was confused when using letters instead of actual number to solve this problem
the goal of this problem is to show that lim x->a x^5=a^5 is true
I will be glad to get some...
Homework Statement
I was trying to show that
1) |a+b|≤|a|+|b|
2) |a+b|≥|a|-|b|
and find out how they were true when a,b>0, a,b<0, and a>0,b<0
Homework Equations
1) |a+b|≤|a|+|b|
2) |a+b|≥|a|-|b|
The Attempt at a Solution
For |a+b|≤|a|+|b|
a,b>0
I got that |a+b|=a+b...