Need help with finding deltas algebraically
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Need help with finding deltas algebraically

[From: ] [author: ] [Date: 13-02-03] [Hit: ]
in each case,so you do 1/4 - 0.05 -Find a symmetric interval for x - 4 which includes 1/4 - 0.1/4 - 0.==> 0.So,......
what do you do if you are given f(x)= 1/x, L= 1/4, x sub 0= 4, and epsilon= 0.05?

in each case, find an open interval about x sub 0 on which the inequality |f(x) - L|< epsilon holds. Then give a value for delta > 0 such that for all x satisfying 0 < |x - x sub 0| < delta the inequality |f(x) - L|< epsilon holds.

so you do 1/4 - 0.05 < 1/x < 1/4 + 0.05 and then what?

-
Find a symmetric interval for x - 4 which includes 1/4 - 0.05 < 1/x < 1/4 + 0.05.
1/4 - 0.05 < 1/x < 1/4 + 0.05
==> 0.2 < 1/x < 0.3
==> 10/3 < x < 10/2
==> -2/3 < x - 4 < 1
==> |x - 4| < 2/3.

So, we can take δ = 2/3 (or any smaller positive number).

I hope this helps!
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