Limit of Signum (sin x)...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:

48. Part *a)==>(i) and (ii)

Part (b).

Part (c).

 

[MathLover1]

a.

see the graph, as x->0 from the right

b. use the graph to see the limit

x->0 from the left (at x=0 is a hole, the first value for limit is -1)

c. graph of g(x)=sgn(sin(x))

 

[nycmathguy]

a.

see the graph, as x->0 from the right

b. use the graph to see the limit

x->0 from the left (at x=0 is a hole, the first value for limit is -1)

View attachment 2574

c. graph of g(x)=sgn(sin(x))

View attachment 2575

1. Thank you for your help.

2. I will surely need your help like never before in Section 1.7. In the next section we are introduced to the Formal Definition of a Limit in terms of delta and epsilon. The delta-epsilon method is a nightmare to most students taking Calculus 1.

3. As you already know, I decided to stop College Algebra for now but for some strange reason, I miss the course. How can I study BOTH Calculus 1 and College Algebra at the same time? Any ideas?

 

[MathLover1]

do it parallel

The real issue you may face is with trig. Calculus I students have to be good with trig graphs, equations and identities. My experience is that beginning calculus students are very poor with equations and graphs using the trigonometric functions. So, do trig graphs, equations and identities too.

 

[nycmathguy]

do it parallel

The real issue you may face is with trig. Calculus I students have to be good with trig graphs, equations and identities. My experience is that beginning calculus students are very poor with equations and graphs using the trigonometric functions. So, do trig graphs, equations and identities too.

Are you saying to do College Algebra at the same time that I am studying Calculus 1? In addition, study trigonometric graphs, equations and identities. Ok. Will do just that....

 

[nycmathguy]

do it parallel

The real issue you may face is with trig. Calculus I students have to be good with trig graphs, equations and identities. My experience is that beginning calculus students are very poor with equations and graphs using the trigonometric functions. So, do trig graphs, equations and identities too.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Does the signum function appear in Calculus 2 and 3? Same question for the step function.

 

[MathLover1]

remember: The signum function of a real number x is a piecewise function which is defined as follows:

graph

that is simple one
Calculus 2, you do advanced limit techniques
calculus 3, limits involving functions of more than one variable

certainly you will face sgn x there too
,

 

[nycmathguy]

remember: The signum function of a real number x is a piecewise function which is defined as follows:

View attachment 2656

graph
View attachment 2657

that is simple one
Calculus 2, you do advanced limit techniques
calculus 3, limits involving functions of more than one variable

certainly you will face sgn x there too
,

Thank you. It has been said that most students struggle in Calculus 2 even more so than when taking Calculus 1 and 3. If this is true, why?

 

[MathLover1]

In the United States, Calculus I typically covers differential calculus (in one variable), plus related topics such as limits. Calculus II typically covers integral calculus in one variable. Calculus III is the term for multivariate calculus, and is an introduction to vector calculus.

Present calculus students, the overwhelming consensus (72% of poolers) is that Calculus 3 is indeed the hardest Calculus class. This is contrary to the popular belief that Calculus 2 is the hardest Calculus class

 

[nycmathguy]

In the United States, Calculus I typically covers differential calculus (in one variable), plus related topics such as limits. Calculus II typically covers integral calculus in one variable. Calculus III is the term for multivariate calculus, and is an introduction to vector calculus.

Present calculus students, the overwhelming consensus (72% of poolers) is that Calculus 3 is indeed the hardest Calculus class. This is contrary to the popular belief that Calculus 2 is the hardest Calculus class

Perhaps Calculus 2 was the hardest course for students back in the day. We can also say that Calculus in general is hard for students whose major requires knowledge of derivatives and integration but who are not majoring in mathematics. Also, the name Calculus is intimidating. Why this name for a math course?

 

[MathLover1]

I don't now why is this name used here, in Europe is not

In Latin, calculus means “pebble.” Because the Romans used pebbles to do addition and subtraction on a counting board, the word became associated with computation. Calculus has also been borrowed into English as a medical term that refers to masses of hard matter in the body, such as kidney stones.

 

[nycmathguy]

I don't now why is this name used here, in Europe is not

In Latin, calculus means “pebble.” Because the Romans used pebbles to do addition and subtraction on a counting board, the word became associated with computation. Calculus has also been borrowed into English as a medical term that refers to masses of hard matter in the body, such as kidney stones.

Ok. Interesting information. Thanks.