Limit of Greatest Integer Function...2

[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:

54. Please do part (b)==>(i) as a guide for me to do the rest. How is part (c) done?

 

[MathLover1]

b.

=

 

[nycmathguy]

b.
View attachment 2588

=View attachment 2589

Easier than it looks. The cos (0) = 1.

 

[nycmathguy]

b.
View attachment 2588

=View attachment 2589

Can you do (a) for me?

 

[nycmathguy]

b.
View attachment 2588

=View attachment 2589

I don't understand part (c).

 

[MathLover1]

part b (i)

lim ([[cos(x)]],x->0) =1

b. (ii)

= 1

b. (iii)

=1

b. (iv)

=1

 

[nycmathguy]

part b (i)

lim ([[cos(x)]],x->0) =1

b. (ii)
View attachment 2635= 1

b. (iii)
View attachment 2636=1

b. (iv)

View attachment 2637=1

I didn't do so well here. I will post more limits of the signum and step functions when time allows for extra practice.