- #1
chez_butt23
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Homework Statement
Limit a[itex]\underline{}n[/itex] as n→∞ = a. Find the limit a, and Determine N so that absolute value(a[itex]\underline{}n[/itex] - a) < [itex]\epsilon[/itex] for all n>N for the given value of [itex]\epsilon[/itex].
The problem that I am working on is:
a[itex]\underline{}n[/itex] = 1/n , [itex]\epsilon[/itex] = 0.01
I'm sure this is very simple, as I am only two weeks into my university's basic calcuus class, but I am not nderstanding what to do. I have also tried going to tutoring and office hours, but my professor only confuses me more with his broken English.
Homework Equations
I am not sure what N is. I know that n is the nmber we are currently plugging in. I also know that a[itex]\underline{}n[/itex] is the whatever equation we are using (in this problem it is 1/n), and I know that [itex]\epsilon[/itex] is a margin above and below the limit.
The Attempt at a Solution
I saarted with the equation:
absolute value((a[itex]\underline{}n[/itex]) - a) <[itex]\epsilon[/itex]
I then plugged in numbers to get:
absolute value ((1/n)-0) < 0.01
After dropping the absolute value (because the limit is zero, and I think I am only solving for positive[itex]\epsilon[/itex]), and isolating n, I proceeded to get:
100 < n
I do not know what to do from here. I am not sure what n>N means or how to solve for it. Thank you so much.