The discussion revolves around the epsilon-delta definition of limits in calculus, specifically focusing on finding a delta (δ) in relation to a given epsilon (ε) for the function f(x) = 3x + 1 at the point x = 1.
Some participants affirm the correctness of the solution provided, while others suggest that the original poster could have framed their question differently to reflect their uncertainty. The conversation indicates a supportive environment, with acknowledgment of the challenges faced in building self-confidence in mathematical reasoning.
There is an underlying theme of personal struggle with self-confidence affecting the approach to problem-solving in mathematics. Participants are navigating both the mathematical concepts and the emotional aspects of learning.
Bolz said: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?
pasmith said:Nothing. Your solution is correct.
HallsofIvy said: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.