You are so kind to share your knowledge and teaching with us. I have chem this semester along with calculus and a part-time job that just drains me, but I am able to catch up with the work with the help of your videos like I did with advanced functions. I am forever grateful for you and for your teaching and taking the time to do these videos, you saved my grades, literally!
Oh Zaina! I’m so glad that I could help you out. It must be very hard to do two condensed courses AND work. I wish you all the best in your studies. Feel free to ask questions ❤️
This is the last chapter of my Course: Vectors and Calculus (MCV4U) and I would like to personally thank you very much for uploading these helpful videos. You are a great teacher and I am very glad I found you! Thank you once again for making the time for us and putting in your great effort to make a difference in other people's lives. All the way from Qatar, Manar
Well, that really made my day! Thank you so much Manar, for taking the time to comment. I will continue to do my best teaching to help the younger students now as well. All the best in your future studies and hope that my lessons will serve you well as you move on to university. All the way from Ottawa! : )
Hello Ms Havrot, in the function y=e^x, is there a horizontal asymptote? According to the Nelsons Textbook, horizontal asymptote exists when both the positive infinity and negative infinity are approaching the same y-value. In the function y=e^x, only the negative infinity is approaching 0, and the positive infinity is not approaching any y-value. Thank you for your attention!
I am happy to find you, Ms Havrot and relearn stuff I loved many years ago in school, but struggled with. Now I want to learn and I find that I understand you.
For example, say we have 5^)-x^2 and we want to find f'(x), would you rewrite it as such: 5^)-x^2 (ln 5) (-2x). So you rewrite the function, write the ln of the base, and then find the derivative of the exponent. Thanks!
Hello Ms. Havrot, I am kind of confused about the derivative part of the second term for Q5. I don't understand why the exponent would be 2x, shouldn't be 2x-1?
No, you need to remember that e is a number. That means that you are dealing with exponentials and the power rule does not apply. The derivative of e^f(x) is e^ f(x) x f’(x)
For y = e^x as you know, the horizontal asymptote is y=0. Therefore any vertical shift of the function will move the horizontal asymptote. So if you have the function y = e^x + 5, the horizontal asymptote will be y = 5
Please let me know where you introduce the ho di hi, hi di ho rule. I am just starting out after many 6years and struggling a bit, and I'd like to know this rule and examples of its usage. KINDLY direct me to a basic lesson where this is introduced
how do I convert y=e^x to log and then into ln? IDK how to do this and its really bugging me... I feel like its log to the base of e of y=x, but that looks wrong.
Why would you want to convert into log first? When you have e^x you can simply use the natural logarithm which is lnx. If you have a specific example maybe I can help you. Otherwise you may want to check out a video that I am working on which does some applications (5.3) I'll be doing that before the day is over ... I hope!
Be careful here. The function y = e^x and the function y = ln(x) are NOT the same functions. That means that it isn't possible to 'convert' one into the other. These two functions are inverses of one another, so there is a kind of connection between them, but they are not the same. There is a process that allows you to FIND the inverse of a given function (which you likely would have learned already), but this isn't the same as CONVERTING from one to the other. If you are asking how to generally convert from exponential to logarithmic form (which isn't the same as turning an exponential function into a logarithmic one), then there is a kind of rule you can follow: If a = b^c (this is exponential form), then this can be rewritten as log_b(a) = c (this is logarithmic form). Note that the underscore used here indicates that b is a subscript (it is written smaller and lower on the line). How can we use this for functions? Well, if you are trying to find the inverse of an exponential function, let's say y = e^x, then first you must swap the x and y variables in the equation of the function (this is just a part of the process of finding an inverse). Then you would isolate for y again. After, you just need to know that if you have a logarithm with a base of e, we write 'ln' instead of 'log'. It would look like this... y = e^x (this is the original function that we want to find the inverse of) x = e^y (this is now the inverse of the original, but we usually like to have y isolated, so...) log_e(x) = y (we use the the conversion between exponential and logarithmic form I discussed above to isolate) y = ln(x) (this is how we would write the equation of the inverse of the original function)
You know there can not be a VA because even though you may be thinking that this function can also be written as 1/e^x^2 the denominator can never be equal to zero. Think about the graph of e^x; it is always positive (in fact it has a horizontal asymptote at y = 0) and never zero, likewise e^x^2 can not be equal to zero. Does that help?
You are so kind to share your knowledge and teaching with us. I have chem this semester along with calculus and a part-time job that just drains me, but I am able to catch up with the work with the help of your videos like I did with advanced functions. I am forever grateful for you and for your teaching and taking the time to do these videos, you saved my grades, literally!
Oh Zaina! I’m so glad that I could help you out. It must be very hard to do two condensed courses AND work. I wish you all the best in your studies. Feel free to ask questions ❤️
Even when you're under the weather, you still put out incredibly helpful content for us, students! Thanks so much, Ms Havrot!!
You are most welcome! It was my retirement project ❤️ So happy that it is successful and helping so many. Thanks to all of you who watch and learn 😊
Tomorrow is my final test before the exam in this course. Thank you for all your wonderful videos! I don't think I would be passing without them.
Good luck!!
This is the last chapter of my Course: Vectors and Calculus (MCV4U) and I would like to personally thank you very much for uploading these helpful videos. You are a great teacher and I am very glad I found you!
Thank you once again for making the time for us and putting in your great effort to make a difference in other people's lives.
All the way from Qatar,
Manar
Well, that really made my day! Thank you so much Manar, for taking the time to comment. I will continue to do my best teaching to help the younger students now as well. All the best in your future studies and hope that my lessons will serve you well as you move on to university. All the way from Ottawa! : )
Hello Ms Havrot, in the function y=e^x, is there a horizontal asymptote? According to the Nelsons Textbook, horizontal asymptote exists when both the positive infinity and negative infinity are approaching the same y-value. In the function y=e^x, only the negative infinity is approaching 0, and the positive infinity is not approaching any y-value. Thank you for your attention!
You must have misunderstood the textbook. A horizontal asymptote does not have to be approached as x approaches both positive and negative infinity
@@mshavrotscanadianuniversit6234 I see! I saw the word OR! I am sorry about that, Ms Havrot.
The textbook said a horizontal asymptote exists if the pos infinity or neg infinity approaches a certain y-value.
Lots of squirrels in my backyard that like to eat bird food too lol! Great vids! Thanks!
Ah, yes … squirrels everywhere! Haha
I have found a safe window feeder that the squirrels just can’t reach and now I feel sorry for them 🤣
I am happy to find you, Ms Havrot and relearn stuff I loved many years ago in school, but struggled with. Now I want to learn and I find that I understand you.
That’s awesome Sally! Feel free to ask any questions that you have 😊
Are you okay Mrs. Havrot? Your voice seems a little dry in this video 😂. Hope your doing better!
Thanks for your concern. I was having some trouble with my voice. I’m good!
awesome video! Super clear and easy to understand : )
Hi Ms Harvot. I notice the at 16:20 how you took the derivative of e^)-x^2 but would this same process also apply if e was just a number, say 4?
For example, say we have 5^)-x^2 and we want to find f'(x), would you rewrite it as such: 5^)-x^2 (ln 5) (-2x). So you rewrite the function, write the ln of the base, and then find the derivative of the exponent. Thanks!
yes ... exactly The derivative of f(x) = a ^x is f'(x) = a^x * ln a and if it is f(x) = a^g(x) then
f'(x) = a^g(x) ln a * g'(x)
Hello Ms. Havrot, I am kind of confused about the derivative part of the second term for Q5. I don't understand why the exponent would be 2x, shouldn't be 2x-1?
No, you need to remember that e is a number.
That means that you are dealing with exponentials and the power rule does not apply. The derivative of e^f(x) is e^ f(x) x f’(x)
Is there a method to finding the horizontal asymptote for e^x? For example with rationals
For y = e^x as you know, the horizontal asymptote is y=0. Therefore any vertical shift of the function will move the horizontal asymptote. So if you have the function y = e^x + 5, the horizontal asymptote will be y = 5
19:53
That's an unfortunate looking mustache Mrs.Havrot :(
haha
THE BEST !!!
Thank you ☺️
Please let me know where you introduce the ho di hi, hi di ho rule. I am just starting out after many 6years and struggling a bit, and I'd like to know this rule and examples of its usage. KINDLY direct me to a basic lesson where this is introduced
th-cam.com/video/_HRT0AouBZw/w-d-xo.html
Here’s the link to the lesson 😊
Great video!
Thanks! Hope you find many others that help to clarify topics for you 😊
how do I convert y=e^x to log and then into ln? IDK how to do this and its really bugging me... I feel like its log to the base of e of y=x, but that looks wrong.
Why would you want to convert into log first? When you have e^x you can simply use the natural logarithm which is lnx. If you have a specific example maybe I can help you. Otherwise you may want to check out a video that I am working on which does some applications (5.3) I'll be doing that before the day is over ... I hope!
Be careful here. The function y = e^x and the function y = ln(x) are NOT the same functions. That means that it isn't possible to 'convert' one into the other. These two functions are inverses of one another, so there is a kind of connection between them, but they are not the same. There is a process that allows you to FIND the inverse of a given function (which you likely would have learned already), but this isn't the same as CONVERTING from one to the other.
If you are asking how to generally convert from exponential to logarithmic form (which isn't the same as turning an exponential function into a logarithmic one), then there is a kind of rule you can follow:
If a = b^c (this is exponential form), then this can be rewritten as log_b(a) = c (this is logarithmic form). Note that the underscore used here indicates that b is a subscript (it is written smaller and lower on the line).
How can we use this for functions? Well, if you are trying to find the inverse of an exponential function, let's say y = e^x, then first you must swap the x and y variables in the equation of the function (this is just a part of the process of finding an inverse). Then you would isolate for y again. After, you just need to know that if you have a logarithm with a base of e, we write 'ln' instead of 'log'. It would look like this...
y = e^x (this is the original function that we want to find the inverse of)
x = e^y (this is now the inverse of the original, but we usually like to have y isolated, so...)
log_e(x) = y (we use the the conversion between exponential and logarithmic form I discussed above to isolate)
y = ln(x) (this is how we would write the equation of the inverse of the original function)
for 15:56 how did you know that there isn't any V.A.?
You know there can not be a VA because even though you may be thinking that this function can also be written as 1/e^x^2 the denominator can never be equal to zero. Think about the graph of e^x; it is always positive (in fact it has a horizontal asymptote at y = 0) and never zero, likewise e^x^2 can not be equal to zero. Does that help?
HI Ms Havrot is this last chapter on gr12 calculus?
Yes. I will do another "optional" lesson on implicit differentiation and maybe related rates which are not part of the Ontario grade 12 curriculum.
The next chapter in this book is the vectors part of the course.
@@mshavrotscanadianuniversit6234 Thank u so much Ms Havrot it's help me a lot !
@@mshavrotscanadianuniversit6234 is vectors easier than the calculus section?
@zinkai1490 it’s different. I think if you have taken physics you will find it easy.