Precise definition of a limit

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| <delta correct to four decimals round down if necessary

Mark44

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.

step1536

Use the given graph of(x) =x^2 |x^2-1| < 1/2 whenever |x-1| <delta .The Given points on the graph are(0.8,0.5), (1.2,1.5). Please give your answer to the value of delta, where deltaor any smaller positive number will satisfy all conditions. correct to four decimals, round down if necessary.

Mark44

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.