I find often that many professors are not good teachers, but I can tell that you genuinely have a passion for TEACHING!!!! Amazing video series, you are going to be an amazing resource for me this semester and I'm so thankful !!!!!
I've watched more than my share of math tutorials and it's probably known to you as well that MOST of the instructors, to put it mildly, utilize chicken scratch to show their work. I want to both thank and congratulate you on your penmanship that makes your already clear demonstrations a much more enjoyable experience than what is typical in this medium.
Why thank you, I do make an effort to keep things as neat and organized as possible when I teach-we don’t need to make the learning process any more difficult than necessary. I appreciate your kind comment and support!
Thank you so much for making these videos!!! You are single-handedly guiding me (and many others I'm sure) through my calculus I class. The fact that you take the time to explain why things happen in each section (and do so with humor) makes the concepts much less intimidating to learn and apply. You're awesome! 😸
Professor V., thank you once again for another awesome lecture on The Limit of a Function in Calculus One. I am relearning Calculus One in fine detail. The examples are very helpful from a theoretical and practical point of view.
You are one of the best math teachers. Thank you. I have an exam on Tuesday and I am watching your videos as I don't understand my professor. Thank you, again.
@@mathwithprofessorv Oh, are we using the 5 because we're talking about the limit as x approaches 5? If so, what is the relevance of the -1? or am I completely off base haha!
Glad you like them! I think you’ll really enjoy relearning Calculus without the pressure of exams etc and be able to appreciate its beauty more since you’re doing it for yourself. Enjoy the journey! ☺️
You pluge in numbers close to the number you want to look for.....if you want 2 for a point X then you plugging 1, 1.9999 and 3, 2.0001. Numbers closer to the point you want. Hope, this makes it clear.
...Good evening Professor V, I hope you're doing well. I'm impressed with your presentation on limits of functions (not the easiest topic for many folks). I just wanted to ask you one brief question about this subject, if I may. Of the function f(x)=1/x, we know from your presentation that the two-sided limit (x--->0) does not exist (DNE). Now suppose that is given the function g(x)=1/x^2. Of course you know this graph very well. How would you write down the outcome of the two-sided limit (x--->0) of g(x), given that the left-sided and the right-sided limits (x--->0) of g(x) both go to positive infinity. However infinity in general is not a real number, but a concept! Undefined or Positive infinity as the answer to my question? Professor V, I'm very curious about your answer, because I believe that in this case with g(x)=1/x^2 there exist different opinions, circulating within the math community, of which you are a part! Thank you again for your clear and precise presentation of "Limits"... Pleasant summer day, Jan-W
Hello Jan-W! Thank you for your thoughtful comment, I love how deeply you analyze and ponder this beautiful subject of Calculus. You are correct that there exist different opinions on this limit, and I did also consult with Professor A to get her opinion on the matter (she and I are in agreement, if you were curious). In terms of the definition of a limit, the limits as x approaches 0 for 1/x^2 does not exist since the limit does not exist as a finite number. However, I do require that my students be more specific (whenever possible) and not simply write "does not exist" for every case. For this particular problem, I would instruct them to answer that the limit is positive infinity, since we are able to more precisely identify how the function behaves near x=0. This is very different than f(x) = 1/x, as you pointed out, since the limit from the left hand side of 0 is negative infinity, which does not match the limit from the right hand side of 0. The matter can be confusing, because the textbook we currently use (James Stewart's Calculus) lists the answer for both limits to be DNE, but my students don't seem to have much trouble when I explain the difference to them. When we move on to study continuity, I repeatedly use the phrase that the "limit needs to exist as a finite number" to help solidify the concept. What are your thoughts on this limit? Thank you again for sparking such an interesting discussion! Take care, Professor V.
Hello Jan-W! Professor A was asking how you were and I told her I hadn’t heard from you in a while. I hope all is well! Feel free to email me: mathwithprofessorv@gmail.com if you like.
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
I find often that many professors are not good teachers, but I can tell that you genuinely have a passion for TEACHING!!!! Amazing video series, you are going to be an amazing resource for me this semester and I'm so thankful !!!!!
Thank you so much, and I’m so happy you found my channel!!!! Happy to help you through your calculus journey! ☺️☺️🫶🏻🫶🏻🫶🏻
Hi I have a question. How did you get -4.56 by using -0.7? How did you go in calculator? Thank you!
I've watched more than my share of math tutorials and it's probably known to you as well that MOST of the instructors, to put it mildly, utilize chicken scratch to show their work. I want to both thank and congratulate you on your penmanship that makes your already clear demonstrations a much more enjoyable experience than what is typical in this medium.
Why thank you, I do make an effort to keep things as neat and organized as possible when I teach-we don’t need to make the learning process any more difficult than necessary. I appreciate your kind comment and support!
Thank you so much for making these videos!!! You are single-handedly guiding me (and many others I'm sure) through my calculus I class. The fact that you take the time to explain why things happen in each section (and do so with humor) makes the concepts much less intimidating to learn and apply. You're awesome! 😸
You’re so welcome! I’m so glad the videos are helpful. 😊
Professor V., thank you once again for another awesome lecture on The Limit of a Function in Calculus One. I am relearning Calculus One in fine detail. The examples are very helpful from a theoretical and practical point of view.
Thank you George! Enjoy relearning Calculus-must be a nice feeling to do so on your own pace and terms!
You are one of the best math teachers. Thank you. I have an exam on Tuesday and I am watching your videos as I don't understand my professor. Thank you, again.
You’re so welcome!!!! I hope your exam goes well 🙏🏻💕💕
that bit around 23:45 or 23:40 where she is talking about where the stick figure's walking has me rolling
Happy to entertain 😉
this video is so so useful for intro to calc and limits! the analogy of the people walking on the graph is super helpful LOL thanks always!
Glad you enjoyed it! You’re so welcome ☺️
yeh I am from INDIA what awesome lecture..help a lot to me thank u professor..
You’re so welcome! ☺️
Professor V you are a lifesaver
It is my honor and pleasure 😊💕
@@mathwithprofessorv At 27:09, can I ask... Why did we use -1 and 5 on the number line, instead of 1 and -5?
@@mathwithprofessorv Oh, are we using the 5 because we're talking about the limit as x approaches 5? If so, what is the relevance of the -1? or am I completely off base haha!
I love your handwriting!!
Thank you so much!
I’m looking to re-learn Calculus for fun, your videos are great!
Glad you like them! I think you’ll really enjoy relearning Calculus without the pressure of exams etc and be able to appreciate its beauty more since you’re doing it for yourself. Enjoy the journey! ☺️
@@mathwithprofessorv Thanks, exactly! 😀
9:00 how are you choosing which values to plug into on both sides?
You pluge in numbers close to the number you want to look for.....if you want 2 for a point X then you plugging 1, 1.9999 and 3, 2.0001. Numbers closer to the point you want.
Hope, this makes it clear.
Thank You, Professor V
You are very welcome 🤗
...Good evening Professor V, I hope you're doing well. I'm impressed with your presentation on limits of functions (not the easiest topic for many folks). I just wanted to ask you one brief question about this subject, if I may. Of the function f(x)=1/x, we know from your presentation that the two-sided limit (x--->0) does not exist (DNE). Now suppose that is given the function g(x)=1/x^2. Of course you know this graph very well. How would you write down the outcome of the two-sided limit (x--->0) of g(x), given that the left-sided and the right-sided limits (x--->0) of g(x) both go to positive infinity. However infinity in general is not a real number, but a concept! Undefined or Positive infinity as the answer to my question? Professor V, I'm very curious about your answer, because I believe that in this case with g(x)=1/x^2 there exist different opinions, circulating within the math community, of which you are a part! Thank you again for your clear and precise presentation of "Limits"... Pleasant summer day, Jan-W
Hello Jan-W! Thank you for your thoughtful comment, I love how deeply you analyze and ponder this beautiful subject of Calculus. You are correct that there exist different opinions on this limit, and I did also consult with Professor A to get her opinion on the matter (she and I are in agreement, if you were curious). In terms of the definition of a limit, the limits as x approaches 0 for 1/x^2 does not exist since the limit does not exist as a finite number.
However, I do require that my students be more specific (whenever possible) and not simply write "does not exist" for every case. For this particular problem, I would instruct them to answer that the limit is positive infinity, since we are able to more precisely identify how the function behaves near x=0. This is very different than f(x) = 1/x, as you pointed out, since the limit from the left hand side of 0 is negative infinity, which does not match the limit from the right hand side of 0. The matter can be confusing, because the textbook we currently use (James Stewart's Calculus) lists the answer for both limits to be DNE, but my students don't seem to have much trouble when I explain the difference to them. When we move on to study continuity, I repeatedly use the phrase that the "limit needs to exist as a finite number" to help solidify the concept.
What are your thoughts on this limit? Thank you again for sparking such an interesting discussion!
Take care,
Professor V.
Hello Jan-W! Professor A was asking how you were and I told her I hadn’t heard from you in a while. I hope all is well! Feel free to email me: mathwithprofessorv@gmail.com if you like.