Use the given graph of f to find a number delta...?

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I'm not really sure what to do here. I think the first step is to set the equation equal to each other?

1 Answer
Max G.
Feb 14, 2018

That's the easy one!

Explanation:

Seriously, you'll like this.
The red horizontal segments are distance 0.2 away from 1. These are #y = 1 - epsilon# and #y = 1 + epsilon#.
The corresponding red vertical segments are at
#x = 1 - 0.3# and #x = 1 + 0.1#.
Choose #delta = 0.1# -- the smaller distance from the limit point. Then whenever
#0 < | x - 1 | < delta#, #f(x)# will be between the red horizontal lines.
In other words, #f(x) - 1 | < epsilon#.

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