Hello everyone. I really need help with these two math problems.
1) The whole concept of "episolon" and "thelta" [not sure if I spelled those two correctly, sorry] confuses me. From what I read in my textbook, it seems that the goal is to "limit" or restrict the given value to a certain area [using vertical and horizontal lines]. Regardless, here is my fruitless attempt at trying to solve this problem.
[part a]
For this first problem, it seems we want the function f(x) to be less than 1 unit from 3, thus making it between 2 and 4. To help us remember this, I drew horizontal lines on my paper at y = 2 and y = 4.
This next step I mimicked from a textbook example; I drew two vertical lines at the points where the graph of f(x) intersected with the horizontal lines I drew earlier. The points where the graph intersects with the horizontal lines is at (2,4) and (10,2).
Thus, is it correct to say that f(x) is less than a unit from 3 on the y-axis if, and only if, x is between 2 and 10? That would lead my maximum value of "thelta" (I'm not sure how to spell it, its that "d" looking figure) to be 7, since 10 - 3 = 7
PLEASE help me out on this, and help me verify the steps I took because I'm not sure if I did this correctly. Now for part b, which I'm equally confused in.
[part b]
Since part b is asking for a value less than 0.5 units away from 3, I'm going to follow similar steps. I will draw my horizontal lines at 3.5 and 2.5. I will then draw my vertical lines at the points where the graph of f(x) intersects with the horizontal lines, which will be at points (3 , 3.5) and (9 , 2.5).
Thus, just like part a, would it be correct to say that f(x) is less than 0.5 unites from 3 on the y-axis if, and only if x is between 3 and 9? That would make maximum value of thelta to be 6, since 9 - 3 = 6.
Again, PLEASE help me confirm this, I am really confused and lost.
For this second one, I honestly have nothing. I read the chapter hoping to find a similar example and found none.
Much thanks in advance to anyone who helps me out here.
1) The whole concept of "episolon" and "thelta" [not sure if I spelled those two correctly, sorry] confuses me. From what I read in my textbook, it seems that the goal is to "limit" or restrict the given value to a certain area [using vertical and horizontal lines]. Regardless, here is my fruitless attempt at trying to solve this problem.
[part a]
For this first problem, it seems we want the function f(x) to be less than 1 unit from 3, thus making it between 2 and 4. To help us remember this, I drew horizontal lines on my paper at y = 2 and y = 4.
This next step I mimicked from a textbook example; I drew two vertical lines at the points where the graph of f(x) intersected with the horizontal lines I drew earlier. The points where the graph intersects with the horizontal lines is at (2,4) and (10,2).
Thus, is it correct to say that f(x) is less than a unit from 3 on the y-axis if, and only if, x is between 2 and 10? That would lead my maximum value of "thelta" (I'm not sure how to spell it, its that "d" looking figure) to be 7, since 10 - 3 = 7
PLEASE help me out on this, and help me verify the steps I took because I'm not sure if I did this correctly. Now for part b, which I'm equally confused in.
[part b]
Since part b is asking for a value less than 0.5 units away from 3, I'm going to follow similar steps. I will draw my horizontal lines at 3.5 and 2.5. I will then draw my vertical lines at the points where the graph of f(x) intersects with the horizontal lines, which will be at points (3 , 3.5) and (9 , 2.5).
Thus, just like part a, would it be correct to say that f(x) is less than 0.5 unites from 3 on the y-axis if, and only if x is between 3 and 9? That would make maximum value of thelta to be 6, since 9 - 3 = 6.
Again, PLEASE help me confirm this, I am really confused and lost.
For this second one, I honestly have nothing. I read the chapter hoping to find a similar example and found none.
Much thanks in advance to anyone who helps me out here.