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A positive number E and the limit L of a function f at a are given. Find a number d such that |f(x) - L| < E if 0 < |x-a| < d.

Lim x --> 5 (1/x) = 1/5; E = 0.05

The answer or value of d = 1/505.

These are the steps that I did, and, unfortunately, my efforts did not end in that result.

|f(x) - (1/5)| < .05 if |x-5| < d.

a. f(5 - d_1) = (1/5) + .05 = 0.25

1/(5 - d_1) = 0.25

d_1 = 1

b. f(5 + d_2) = (1/5) - 0.05 = .15

1/(5 + d_2) = 0.15

d_2 = 1.67

Neither delta fits the answer. Why is my proof terribly incorrect? Is there an alternate method?

Thanks.

Lim x --> 5 (1/x) = 1/5; E = 0.05

The answer or value of d = 1/505.

These are the steps that I did, and, unfortunately, my efforts did not end in that result.

|f(x) - (1/5)| < .05 if |x-5| < d.

a. f(5 - d_1) = (1/5) + .05 = 0.25

1/(5 - d_1) = 0.25

d_1 = 1

b. f(5 + d_2) = (1/5) - 0.05 = .15

1/(5 + d_2) = 0.15

d_2 = 1.67

Neither delta fits the answer. Why is my proof terribly incorrect? Is there an alternate method?

Thanks.

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