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Limit and epsilon question

Posted 9 years ago
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I don't know how to input my question. Please help if you can. The problem is to find the limit of (2n+1)/(n-2) and to find the closest n where epsilon =0,01. Finding the limit is no problem, but how and what I need to input in wolfram alpha to show me the n where is true that epsilon = 0,01. Thank you in advance and happy holidays!

POSTED BY: Lorant Zs

Hello, I am assuming that you want the limit as n->Infinity? If so,

expr = (2 n + 1)/(n - 2)
eqn = expr - Limit[expr, n -> Infinity] == epsilon
sol = Solve[eqn, n]
n /. sol /. epsilon -> 0.01

gives n approximately equal to 502.

Plot[Evaluate[expr - Limit[expr, n -> Infinity]], {n, 490, 510}, 
 PlotRange -> All, Epilog -> Line[{{0, .01}, {1000, .01}}]]
POSTED BY: W. Craig Carter
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