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?
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?
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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!
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!