Limit of Signum 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:

47. Part (a)

Parts (b)==>(i) and (ii).

 

[MathLover1]

as stated in given function, sgn(x)=1 if x>0

so,

and, sgn(x)=-1 if x<0

so,

 

[nycmathguy]

as stated in given function, sgn(x)=1 if x>0

so,

View attachment 2571

and, sgn(x)=-1 if x<0

so,
View attachment 2572

1. What does the graph look like?

2. How about this one below?

Limit of Signum (sin x)...1

 

[MathLover1]

graph:

 

[nycmathguy]

graph:
View attachment 2573

You are wonderful. Please, check the Signum (sin x) link.

 

[nycmathguy]

graph:
View attachment 2573

 

[MathLover1]

47.

a. correct

b.

 

[nycmathguy]

47.

a. correct

b.

View attachment 2634

You know that | sgn (x) | is the absolute value of sgn (x). As we approach 0 from the left and right, the function approaches 1. How is it done algebraically?

 

[MathLover1]

the Signum (sin x)
you now sin (0)=0, so Signum (0) is 1 or -1

 

[nycmathguy]

the Signum (sin x)
you now sin (0)=0, so Signum (0) is 1 or -1

Nice graph. Looks good.