Thread: Limits: Find Delta

Hey, first post here and I just started this calculus I class.

Here's the question:

f(x) = 2 - (1/x)

Find Delta such that if 0 < |x - 1| < Delta then |f(x) - 1| < 0.1

Here's what I have so far:

|f(x) - 1|
= |2 - (1/x) - 1|
= |1 - (1/x)| (my book shows |f(x) - 1| = |(1/x) - 1|)

Originally Posted by bearjew11

Here's the question:
f(x) = 2 - (1/x)
Find Delta such that if 0 < |x - 1| < Delta then |f(x) - 1| < 0.1

You must understand that .
Then

Now if then or

So pick .

Originally Posted by bearjew11

Hey, first post here and I just started this calculus I class.

Here's the question:

f(x) = 2 - (1/x)

Find Delta such that if 0 < |x - 1| < Delta then |f(x) - 1| < 0.1

Here's what I have so far:

|f(x) - 1|
= |2 - (1/x) - 1|
= |1 - (1/x)| (my book shows |f(x) - 1| = |(1/x) - 1|)

Yes that's the same thing: |a- b|= |b- a|
Now you would want to write and .

Now you can say "if then and so you only need an upper bound on |x|. If x is "close to 1", say between 0 and 2, what is the largest |x| can be? What about ?