I remade this video, after watching the original version. I wanted to do the discussion with the hand-written work a little bit better than I did last time. I noticed though, after watching both videos, that the end of the original video, using the Desmos graphs, was actually pretty good. I recommend watching this one, and the end of the original, which is video #40 on the current playlist. Please let me know if you have any questions!

Near 21:00, I talk about a classroom activity in which we graph tangent lines on a grid and estimate the slope. A better way to help us notice the similarity between the derivative and the original function is to include m_estimate as one of the columns in our table. Then the x-values and those estimates can be plotted as (x,y) pairs, and then we'll see that the graph of the derivative (slope function) and the graph of the original function are very similar.

At about 17:50, I start talking about the spacing between the x-values that map to 1 when referring to choosing x-values that map outside the interval (0.9, 1.1). I should have been talking about the x-values that map to any number between -1 and 0.9, (probably those that map to -1 because the calculations were pretty much already done). I noticed some other problems toward the end of the video as well. I'll edit or rerecord and repost it. Sorry about that.

At the beginning of the video, we review the list of known functions that are continous on their domains that were discussed in the previous video. This time, we graph them. At about 17:53, we begin looking at trig functions with vertical asymptotes, so if you're watching this for examples of functions with vertical asymptotes, you might want to start there. I'd like to add a table of values for the infinite limits in these examples as well.

At 35:38, I forgot to multiply the factored by the leading coefficient. The factored form of the quadratic should be a(x-c1)(x-c2).

very thanks!

Has a similar one for an exam, but I was supposed to use unknown coefficients, RIP, nice writeup tough

Very nice explanation ma'am.👍🏻

Thanks 👍

Thank you for your explanations! You've helped out a very stressed student trying to speed learn some algebraic geometry for my masters thesis

thanks mam love from india

many thanks for your video

So for this type of question the mean and sd will always be 0 and 1?

Thanks!!

Wow! Thank You So Much🙏🔥

Thank you @Sasha Townsend!! You have no idea how many lives you've just saved !! Keep up the good work <3 :)

I loved the explaination

Ma'am really helpful, Thank you

Teachers essentially raised me, glad to see they still care to make that difference; and without concern for profit!

fantastic stuff

Thanks very much. This was very accurate and helpful.

Is there a quick way in which the characteristic equation could be found as in variation of parameters problem without having to through all those steps ?

19:10 when were taking second derivative of y2, you wrote e^x twice, otherwise I appreciate you for this video, well explained everything is clear.👏💖❤👌

Buenos días profesora, enseña demasiado bien. Sus notas son ordenadas limpias claras y concisas. Me gustaría saber si tiene alguna presentación, o algún documento en donde pueda encontrar sus notas escaneadas.

Thanku soo much mam,,, you explained very well. It was very informative 😇

Hi sasha, nicely explained

Thanks a lot. Great.

Thank you so much for the clear explanation, I had such a tough time with this problem!

I am an Electrical Engineer from Vietnam, my research suddenly require me to look after abstract algebra and algebraic geometry. Do you have any playlist regarding this topic ? Also what playlist that the this video belong to ?

how would this look on a ti-84, given sample mean, standard deviation, and a 90% confidence interval

THANK YOU!!!!!!!!!!!!

Damn she bad I wish you were my math teacher

I will be using all of these videos for my classes on the 14th. Thank you ❤ Why did I pick engineering 🤣😭

damn you are smart and hot.... Im at uni and I still found some help from you so thanks!

How do I know the graph of the solution of the second order differential equation,I mean that there are some problems about solving the differential equation and then determine the graph of the solution but without using Technology. I hope that was clear Thanks in advance 🌺

Thanks, Prof Townsend, for these great Linear Algebra videos. One of the best teaching styles! Please make more Linear Algebra videos when you have the chance.

Around 28:20, I made a mistake. The power of t should be (n-3) after differentiating y_2 the second time.

thank youuuuuu

A field is quality not quantity. When the Dielectric energy decays from the Inertial plane, Time starts in the Space Universe. Then Dielectric Energy decays into its Dielectric Voidence Field/Magnetism. Magnetism gives Magnitude to the Space Universe. Gravity is opposite, centripetal acceleration of Magnetism/Dielectric Voidence Field into the Dielectric energy, then into the Inertial plane/Counterspace. Tunnels through the Inertial plane into Space. Repeat. Lights rate of induction is the rate of creation of Magnetism. Both transverse waves are needed for lights rate of induction, only Dielectric or Magnetism is not enough. This is why mediated to center of Blackholes/Counterspacial Sinks do not have light. It's only Dielectric Energy at its center, no EM waves can exist. Ken Wheeler and Eric Dollard. Took 4 years of math in high school. Was offered a scholarship in math. Worked union concrete, instead. Maybe a bad choice? Thinking about vortex math. Aether's Dielectric Hyperboloid, separated by its Inertial plane, into 2 vortices. Surrounded by Aether's Magnetic Torus. The Scalable Aether, Casimir Effect Universe! Space and Counterspace are the plates, the Inertial plane attracts and repels the plates. There I go again. You said you were going the explain a field. Ken Wheeler says no PHD can explain a field. Ken teaches Plato's Field Theory. Quantum is wrong.

You're amazing Teacher Sasha Masha Allah , even there wasn't much followers you continued posting videos 🎩 The god love that because he will send a prophet Just for one person Edit : My English hhh I mean this is the way of the god he didn't care if 1 million or 1 person and that happen before I heard that meaning from Dr. Adnan Ibrahim

How do you get the table? Please and thanks

Thank u so much 💯😂❤️

I know I said this in the previous vid already but holy cow am I grateful for you rn. these videos are so so so helpful especially because you go through so many examples. My book is a bit difficult to understand in terms of when an example is just a statement as opposed to an actual worked out question so i never know whether something is a given or whether I need to know how they got it. thanks again Sasha!!!

THANK YOU FOR THEEEEESSSSEEE😭😭🙌🏽🙌🏽loooots of appreciation all the way from South Africa!!

Thank you very much!!

Thank you a lot from Russia

Firstly your videos are great and I find them extremely helpful. I'm an engineering student (mechatronics engg.) from Pakistan and am currently studying Differential equation and transforms in my 2nd semester. One thing I wanted to add is that according to my calculations in expo. order, for M=1 the graph of e^t^2 would dominate the graph of e^ct as soon as t>c is fulfilled. There will be an intersection of curves at t=c and e^ct would dominate for t<c. This means that our T=c for M=1.

Many thanks, Sasha!