# Precise definition of a limit

by step1536
Tags: definition, limit, precise
 P: 20 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution Given points (0.8,0.5), (1.2,1.5) f(x) =x^2 |x^2-1| < 1/2 whenever |x-1|
Mentor
P: 19,694
 Quote by step1536 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution Given points (0.8,0.5), (1.2,1.5) f(x) =x^2 |x^2-1| < 1/2 whenever |x-1|
You have shown an attempt at a solution, but haven't shown the problem itself. This makes it more difficult for us to determine what you're trying to do. Please add this information. Punctuation would be nice, too.
 P: 20 Use the given graph of(x) =x^2 |x^2-1| < 1/2 whenever |x-1|
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P: 19,694

## Precise definition of a limit

That's not much of an improvement over what you had in the first post. Here is what I think the given problem is.
f(x) = x2
Find a value of delta so that when |x - 1| < delta, |x2 - 1| < 1/2.
In other words, how close to 1 must x be so that x2 will be within 1/2 of 1? Draw a graph of the function. On your graph, draw a horizontal line through the point (1, 1). Draw two more horizontal lines, one 1/2 unit above the first line and the other, 1/2 unit below the first line. At the points where these two lines intersect the graph of y = x2 in the first quadrant, draw vertical lines down to the x-axis. The two intervals to the left and right of (1, 0) can help you find what delta needs to be.

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