(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this...

(a) Find the limit of {(1/(n^(3/2)))-(3/n)+2} and use an epsilon, N argument to show that this is indeed the correct limit.

(b) Use an epsilon, N argument to show that {1/(n^(1/2))} converges to 0.

(c) Let k be a positive integer. Use an epsilon, N argument to show that {a/(n^(1/k))} converges to 0.

(d) Show that if {Xn} converges to x, then the sequence {Xn^3} converges to x^3. This has to be an epsilon, N argument [Hint: Use the difference of powers formula].

Expert Solution

Colby Messinger answered 3 years ago

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