Value of Number "a" and Value of Limit

[nycmathguy]

Calculus
Section 2.3

What is the easiest way to do 67?

 

[MathLover1]

=

lim will exist when numerator 3x^2+ax+a+3=0 if x->-2
3(-2)^2-2a+a+3=0
12-2a+a+3=0
15-a=0
a=15

then you have

factor

=

, then limit is

check the graph:

 

[nycmathguy]

View attachment 2984

=View attachment 2985

lim will exist when numerator 3x^2+ax+a+3=0 if x->-2
3(-2)^2-2a+a+3=0
12-2a+a+3=0
15-a=0
a=15

then you have

View attachment 2987


factor View attachment 2990=View attachment 2991, then limit is


View attachment 2992

check the graph:

You said the limit will exist when the numerator equals 0, if x tends to -2. What information in the problem told you to equate the numerator to 0? What clue indicates that this is the first step to find the value of the number "a"?

Stay tuned for more math later. You forgot to answer one question in terms of evaluating limits. I included that thread in one of my replies today. This means two more questions will be posted on Saturday to keep our journey at no more than 3 questions per thread.

Keep in mind that my questions from the new textbook are not NOT COVERED OR TAUGHT by Jenn. Like I said before, it is a waste of time to post problems that I already know how to do. Agree?

In terms of the Epsilon-delta definition of a limit, I will post several threads when we get there in the new Calculus textbook I downloaded a few days ago. I want you to reply in detail to all Epsilon-delta definition of a limit problems for me to file in my study notes should I ever desire to learn this early method of proofs in Calculus 1.

 

[MathLover1]

you can find the value of "a" when the numerator equals 0, assuming x = -2, then you check a lim for the value of "a" you get and you will see that both numerator and denominator will be equal to 0, so you got li equal to 0/0 which is undefined
in that case you are taking derivative

 

[nycmathguy]

you can find the value of "a" when the numerator equals 0, assuming x = -2, then you check a lim for the value of "a" you get and you will see that both numerator and denominator will be equal to 0, so you got li equal to 0/0 which is undefined
in that case you are taking derivative

According to Jenn, when we get 0/0, we can find the limit without taking the derivative. This is what I am learning Jenn now. The video lesson is called Indeterminate Forms.

 

[MathLover1]

btw, how Jenn's site working for you?

 

[MathLover1]

0/0 is the limit you get without taking the derivative

 

[MathLover1]

According to Jenn, when we get 0/0, we can find the limit without taking the derivative. This is what I am learning Jenn now. The video lesson is called Indeterminate Forms.

the concept of L'hopital's rule and how to use it to evaluate limits associated with indeterminate forms of zero and infinity
so, if you can't find lim, take derivative

 

[nycmathguy]

btw, how Jenn's site working for you?

I am learning so much watching her videos. Today, I finished taking notes on the Squeeze Theorem and Limits at Infinity. I feel very comfortable with her teaching method.

The $179/year is totally worth it. I should be done with Calculus 1 and 2 before next April. I will renew my membership each year at $179 to take notes on additional courses like Calculus 3, Linear Algebra, Differential Equations, Statistics and Probability and Discrete Mathematics. After taking notes on all the courses listed here, I will then end my yearly membership. In any case, why do you ask?

 

[nycmathguy]

the concept of L'hopital's rule and how to use it to evaluate limits associated with indeterminate forms of zero and infinity
so, if you can't find lim, take derivative

I will post a sample of 0/0 and how to find the limit without taking the derivative. L'Hopital's Rule is covered by Jenn when we get to derivatives. We are still in the limits section of her Calculus 1 video lessons.

 

[nycmathguy]

0/0 is the limit you get without taking the derivative

 

[MathLover1]

correct

So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

 

[MathLover1]

I am learning so much watching her videos. Today, I finished taking notes on the Squeeze Theorem and Limits at Infinity. I feel very comfortable with her teaching method.

The $179/year is totally worth it. I should be done with Calculus 1 and 2 before next April. I will renew my membership each year at $179 to take notes on additional courses like Calculus 3, Linear Algebra, Differential Equations, Statistics and Probability and Discrete Mathematics. After taking notes on all the courses listed here, I will then end my yearly membership. In any case, why do you ask?

are you just watching her videos or you can ask her questions directly if you have any?

 

[nycmathguy]

correct

So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

I know what L'Hopital's Rule is and what it's for. I just don't want to skip any video lessons or sections in my study. I paid $179 for a year. I want to see every video by Jenn.

She covers L'Hopital's Rule in a future video lesson when we get to derivatives. My threads here, as I explained last week, will come from the textbook and will consist of problems not covered by Jenn in her video lessons.

 

[MathLover1]

The $179/year is totally worth it only if she is in contact with you and give you more detailed explanation if you need it.
So, what is she giving you except videos to watch???

 

[nycmathguy]

The $179/year is totally worth it only if she is in contact with you and give you more detailed explanation if you need it.
So, what is she giving you except videos to watch???

The $179/year includes contact with Jenn if I need extra help in terms of understanding what she is teaching. The yearly membership fee does not include reaching out to Jenn about material in my textbooks. Luckily, I understand every video lesson thus far. So, there is no need to contact Jenn. I am taking notes. I am a decent note-taker.

I will say this, however, Jenn has staff working for her at calcworkshop.com in terms of answering text messages about the website, membership fees, what each membership has to offer, etc. I contacted the website many times before joining and my messages have been ignored. Maybe you will have better luck. I think it's unprofessional for a website to have a contact link to disregard messages from students who are interested in joining.

You say?

 

[MathLover1]

does Jenn use different textbook?

 

[nycmathguy]

does Jenn use different textbook?

I don't know which textbook she uses but questions are legitimate. I think she has her own set of textbooks. She is not just a tutor. Jenn is a licensed teacher of mathematics. I think she has an M.A. or M.S. in Mathematics. I am trying to learn more about Jenn and her teaching background but thus far, her staff is not responding to my messages. What can I do? What should I do?

 

[nycmathguy]

are you just watching her videos or you can ask her questions directly if you have any?

1. I am NOT just watching her videos.

2. I am taking notes along the way.

3. No need to contact Jenn so far. Lessons have been pretty easy.

4. Unlike professor Leonard, Jenn provides the needed steps along the way for each problem solved on video.

5. Jenn works out lots of problems with steps along the way. I have not come across anyone on YouTube using steps.

I am upset, however, that her staff is not responding to my text messages. This is unprofessional. Those people should be questioned by Jenn.

You say?

Can you do me a favor? I want you to contact Jenn's staff pretending to be a student with questions about the website, Jenn's teaching method, her textbook(s), etc.

You say?

 

[MathLover1]

she has her own set of textbooks for sure, but why you do not as her what they are?

if her staff is not responding to my messages, then leave
it doesn't make sense to be there and watch videos for 179.00 if you have plenty other videos to watch for free