1 Attachment(s)

Problem with defining Delta

How would I go about something like this?

Attachment 27051

Edit: I guess what I'm looking for is a detailed and intuitive walk-through so that I can apply those techniques to the remainder of the similar problems. I missed this class and it's important to me to know every detail.

Re: Problem with defining Delta

Can you point out an x such that the distance from x to 1, i.e., |x - 1|, is 0.2 and the distance from f(x) to f(1), i.e., |f(x) - f(1)|, is greater than 0.2?

Edit: Changed |f(x) - f(x)| into |f(x) - f(1)|.

Re: Problem with defining Delta

I'm sorry. I'm not sure what you mean. Can you explain?

Re: Problem with defining Delta

I fixed a typo in post #2.

The question is as simple as it goes. I don't see how to simplify it. I would invite you to show the exact phrase you don't understand or otherwise describe your difficulty.

Perhaps you can answer the following questions.

Do you understand that the distance between two points (x1, 0) and (x2, 0) along the x-axis is |x1 - x2|? Similarly, the distance between (0, y1) and (0, y2) along the y-axis is |y1 - y2|.

What is f(1.2) approximately?

What is the approximate distance between f(1.2) and f(1), i.e., what is |f(1.2) - f(1)|?