This question doesn't make sense unless you are given a specific function f! It looks to me like f is some continuous function such that f(3)= 2. But what goes in the blank depends upon exactly what f is. Surely you realized that?MellowOne said:Homework Statement
For the statement "If x is within _______ units of 3 (but not equal to 3), then f(x) is within 0.01 unit of 2," write the largest number that can go in the blank
Homework Equations
Nonr
The Attempt at a Solution
It's a multi-step problem, but the two numbers I ended up with are 1.99 or 2.01. I'm not sure which one fits into this statement because I'm not quite sure what it's asking.
The exclamation point after f was punctuation in the sentence, just like this one!MellowOne said:Sorry, maybe I should have put the function that I was given. I'm not sure what F! means, but here's the function I'm given. F(x) = (x^3 - 7x^2 + 17x - 15)/( x - 3) It is a continuous graph, but at x = 3 there's a point of discontinuity which is (3,2).
You mean that F has a removable discontinuity at x= 3. That's a discontinuity because 33- 7(32+ 17(3)- 15= 27-63+ 51- 15= 78- 78= 0 as well as 3- 3= 0: both numerator and denominator are 0 at x= 3. Because x= 3 makes the numerator 0, we know that x-3 is a factor. Knowing that it is easy to see that x3- 7x2+ 17x- 15= (x-3)(x2- 4x+ 5) so for x NOT equal to 3, this is just F(x)= x2- 4x+ 5= (x-4)(x-1). The discontinuity is "removable" because that has limit 3 at x= 2.MellowOne said:Sorry, maybe I should have put the function that I was given. I'm not sure what F! means, but here's the function I'm given. F(x) = (x^3 - 7x^2 + 17x - 15)/( x - 3) It is a continuous graph, but at x = 3 there's a point of discontinuity which is (3,2).
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