Find a Number Delta...1

[nycmathguy]

Calculus
Section 1.7

Can you work this out step by step as a guide for me to do a few more on my own?

 

[MathLover1]

if you have 0< |x-3| <δ, then

0< |x-3| => x>3 or x<3
and
|x-3| <δ => x = 3, δ>0

when you combine intervals, solution is x>3 or x<3

so, in this case, 0< |x-3| <δ, there is no solution for δ


abs(f(x)-2)< 0.5

Apply absolute rule: If |u|<a, a>0 then -a<u<a

-0.5< f(x)-2< 0.5
2-0.5< f(x)< 2+0.5
-1.5< f(x)< 2.5

 

[nycmathguy]

if you have 0< |x-3| <δ, then

0< |x-3| => x>3 or x<3
and
|x-3| <δ => x = 3, δ>0

when you combine intervals, solution is x>3 or x<3

so, in this case, 0< |x-3| <δ, there is no solution for δ


abs(f(x)-2)< 0.5

Apply absolute rule: If |u|<a, a>0 then -a<u<a

-0.5< f(x)-2< 0.5
2-0.5< f(x)< 2+0.5
-1.5< f(x)< 2.5

Sorry but this remains unclear to me. I will need to study your notes a few more hours and get back to this tomorrow. Show combining the intervals. Show how this is done.