Find Delta...1

[nycmathguy]

Calculus
Section 2.4

Again, this is not taught by Jenn in her videos. I need a detailed reply for 1 and 2. Your reply will be placed in my Calculus files to review when time allows. Thank you very much.

 

[MathLover1]

1.
Given : | x-1| <δ

then |f(x) − 1| < 0.2

To find the number δ then is to find how close x has to be to 1.
In order for f(x) < 0.2 that is close to 1.

or,

How close does x have to be to 1 (on either side), for f(x) to be between 0.8 and 1.2 ?
So, by the graph :
It is to clear that on the left side of x = 1, x can be within 0.3, but on the right side, it’d have to be within 0.1, of 1, for f(x) to be that close to 1.

Now,
f(x) is within 0.2 of 1 ( which is what | f(x) - 1 | < 0.2 is saying),
we take δ=0.1, which is sure to work on both sides.

2. do it same way

 

[nycmathguy]

1.
Given : | x-1| <δ

then |f(x) − 1| < 0.2

To find the number δ then is to find how close x has to be to 1.
In order for f(x) < 0.2 that is close to 1.

or,

How close does x have to be to 1 (on either side), for f(x) to be between 0.8 and 1.2 ?
So, by the graph :
It is to clear that on the left side of x = 1, x can be within 0.3, but on the right side, it’d have to be within 0.1, of 1, for f(x) to be that close to 1.

Now,
f(x) is within 0.2 of 1 ( which is what | f(x) - 1 | < 0.2 is saying),
we take δ=0.1, which is sure to work on both sides.

2. do it same way

Perfect. I will try 2 tomorrow. Jenn does not cover this type of problem. I thank you.