In: Advanced Math
(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].