Limit of Greatest Integer Function...1

[nycmathguy]

Calculus
Section 1.6

Note:

Only do as indicated here. I will work on the rest on my next set of days off.

Please provide a step-by-step step reply to the following:

53. Part(a)==>(i)

Part (b)==>(i)

Part (c)

 

[MathLover1]

a.
lim([[x]]) as x->-2 from the right ( x->-2+)

lets check first number approaching -2 from the right: x=-1.9

on the number line, -1.9 is between 0 and -2, so

b.
lim([[x]]) as x->n from the left

c. exists for x=a

 

[nycmathguy]

a.
lim([[x]]) as x->-2 from the right ( x->-2+)

lets check first number approaching -2 from the right: x=-1.9

on the number line, -1.9 is between 0 and -2, so

b.
lim([[x]]) as x->n from the left

c. exists for x=a

Thank you. I will do the rest and show my work.

 

[nycmathguy]

a.
lim([[x]]) as x->-2 from the right ( x->-2+)

lets check first number approaching -2 from the right: x=-1.9

on the number line, -1.9 is between 0 and -2, so

b.
lim([[x]]) as x->n from the left

c. exists for x=a

 

[MathLover1]

53.
graph looks like this

a.

b.

 

[nycmathguy]

53.
graph looks like this

a.
View attachment 2659

b. View attachment 2660

I forgot to complete b. Yes, the limit is n.

Note: I will need your help big time in Section 1.7. It deals with the epsilon/delta definition of a limit. I have never, ever, never, ever, quite understood this stuff at all. I also don't see the sense in teaching this formal definition of a limit to Calculus 1 students. The material is very scary, to say the least.