Question

Find delta >0 The rest of problem in the pic

Answer 1

I do not see a picture.

Answer 2

I am providing the question as well as the books solution. My question is just help me understand whats going on in the solution. where do they get 4 from???

Answer 3

deltax?

Answer 4

pic included

Answer 5

from the line above

Answer 6

| x- 5 | = | x - 2 - 3 | <= |x -2 | + |-3| by triangle inequality theorem

Answer 7

okay i got the triangle inequality, but dont get the 4 or the 1/12

Answer 8

| x- 5 |
= | x - 2 - 3 |
<= |x -2 | + |-3| by triangle inequality theorem
< 1 / 12 + 3 = 3.08333.. < 4

Answer 9

could i have picked different numbers other than 1/12 and 4

Answer 10

yes, but you would end up with a number less than 1/3 , in the next step

Answer 11

is that bad

Answer 12

which is fine

Answer 13

what about instead of saying 4 say 10 or 100 or 1000. cant i just pick some really big number to be safe

Answer 14

no you dont want bigger than 4, because the next step has to be less than 1/3

Answer 15

does it have to be less than 1/3 or exactly = to 1/3

Answer 16

What happens if we use a less tight bound
if you had | x - 5 | < 5 ,
then the next step would be
| x^2 -7x + 10| = | x - 5| | x - 2 | < 1/12 * 5 = 5/12, which is greater than 1/3

Answer 17

so you cant pick 5. got ya

Answer 18

the biggest you can choose is 4, the least value is 3 + 1/12

Answer 19

thank you. i will now try some of the other problems like this. this really helped!