Limit of Signum Function

[nycmathguy]

Calculus
Section 2.3

Note: The following question is not covered by Jenn in any of her limits video lessons. However, I am curious about how this one is done.

Do the following only:

Part (a) => (iv), (v), and (vi)

Parts (b) & (c)

 

[MathLover1]

Part (a)
(iv)

(v)

(vi)

Parts

(b) a->0

(two-sided limit does not exist)

(c)

 

[nycmathguy]

Part (a)
(iv) View attachment 2934

(v) View attachment 2935

(vi) View attachment 2936

Parts

(b) a->0
View attachment 2937

View attachment 2938
(two-sided limit does not exist)

(c)

How did you conclude on each limit here? Did you use a calculator?

 

[MathLover1]

given

and sin(pi)=0
and

 

[nycmathguy]

given View attachment 2941 and sin(pi)=0
and View attachment 2942

Let me see: sin(0) = 0.

signum(0) = 1 & -1.

As x-->pi from the right, we plug values slightly bigger than pi for x.

As x-->pi from the left, we plug values slightly less than pi for x.

Yes?

 

[MathLover1]

yes

 

[nycmathguy]

yes

This is precisely what I needed to be shown.

 

[nycmathguy]

yes

How many questions should I post at any given time? I don't want to bombard you with lots of math problems. I know that you have a life outside of the math site.

Is 3 questions per day good enough? Is 5 questions per week good enough? What about on Saturday and Sunday? How many questions on Saturday? How many on Sunday? I will wait to hear from you before posting anymore threads.

 

[MathLover1]

3 questions per day is ok

 

[nycmathguy]

3 questions per day is ok

Perfect. Three questions per day (not everyday) will do. This will allow you to be more detailed in your reply to my questions. A more in depth reply per question leads to more information for me.