Finding delta in terms of epsilon-delta definition

[Bolz]

Homework Statement

If f(x) = 3x+1 en assume δ > 0. Assume ε>0.
Give a δ > 0 with the following property :

|x-1|< δ => |f(x) - f(1)| < ε

Homework Equations

The Attempt at a Solution

|f(x) - f(1)| < ε
<=> |3x+1-(3*1+1)| < ε
<=> |3x-3| < ε
<=> |x-1| < ε/3


|x-1| < δ
|x-1| < ε/3


=> δ=ε/3>0


What am I doing wrong?

Thanks in advance!

 

[pasmith]

Homework Statement

If f(x) = 3x+1 en assume δ > 0. Assume ε>0.
Give a δ > 0 with the following property :

|x-1|< δ => |f(x) - f(1)| < ε

Homework Equations

The Attempt at a Solution

|f(x) - f(1)| < ε
<=> |3x+1-(3*1+1)| < ε
<=> |3x-3| < ε
<=> |x-1| < ε/3


|x-1| < δ
|x-1| < ε/3


=> δ=ε/3>0


What am I doing wrong?

Nothing. Your solution is correct.

 

[Bolz]

Nothing. Your solution is correct.

Oh ok. I'm learning this on my own so I assumed it had to be wrong. Self confidence is important in math too apparently..
Anyway, thanks for checking it! :)

 

[HallsofIvy]

Then it would have been better to ask "Is this correct" rather than "What am I doing wrong"! You are not going to do very well assuming that you cannot do the work.

 

[Bolz]

Then it would have been better to ask "Is this correct" rather than "What am I doing wrong"! You are not going to do very well assuming that you cannot do the work.

Sorry, you're right. I'm just struggling with a lot in life and I think my lack of self confidence leaked into doing math. Sorry again.