❖ Taylor and Maclaurin Series - ln(x) ❖

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im glad you fixed the 1/3 at the end, i was trippin balls

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Felt the same entirely.

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I Checked comments too!

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I have my third Calc2 exam tomorrow that I need to get around a 70 on to still have the possibility to pass the class with a C (im a math major, sadly had a bad start this semester) and your videos make this stuff, along with other stuff like the Power series, very easy to learn. THANK YOU SO MUCH!

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[@connorbannen2562]

OMER SALEEM The difference between taylor and maclaurin is that when a=0 it is considered a maclaurin series. The process is exactly the same however. Hope this helps!

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Thanks, it helps.

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Im not sure which way he should take this xD

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No lie, test in 26 min, been staring at the book trying to understand Taylor and Maclaurin Series. Then I remembered there is a guy on youtube that teaches it very clearly. Bam. 10min later I actually get what I have been trying to understand for hours. Good stuff.

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[@konkre1123]

you have no idea just how grateful i am for your video. Ive been searching all over the place for a good description for a taylor/maclourian series video and my book is no help. you are the first to explain it out so i could easily understand it. +1 subscriber

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Signed up for the BC Exam when I'm taking AB. Attempting to learn this stuff in a day. You are saving me man, SAVING ME.

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I seriously watched all you series and sequence videos for this exam tomorrow. I love you. You go slow but i still have to pause it sometimes, and you go over it in concepts so its super easy. This is better than a book. PS im a lefty too *high five*

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This semester I had a terrible teacher. Pretty much had to teach myself calc 2 and all thanks to you i passed the class with a low A. Looking forward to your videos for future math classes. Thank you!

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What a boss, still helping people 11 years later

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You seriously saved my butt. My calc 2 final is in about 20mins and I was up studying the Taylor series until 4am. Thank you so muchI have to make sure I subscribe!!

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your sum-sign (sigma) looks like its written in Metallica-font.

[@nalahbabi]

I was really depressed when i couldnt know why you had (1/3) instead of (1/2) when a=2, and at the end of the video i was really happy when you fixed it , because I would of changed my major from math to something that doesn't has math in it, or at least has easy stuff... thank u very much and I hope u continue doing these great videos for the students and hope that we can do something in return for all of the great videos that u have uploaded online

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excellent! that is a solid return for only 20 minutes worth of vids : )

[@Riotgunner19]

Best explanation on the subject I've seen. Much better than how it was covered in my calculus 2 class.. Great Work!

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@JuniusFaction you are taking it right now as i type this!! i am projecting math thoughts throughout the cosmos... i hope you are getting them!

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An Infinite Series of Thanks! You caught that little error at the end. The rest is beautifully laid out. Pretty amazing stuff, Taylor Series!

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[@patrickjmt]

yes, as pointed out in the annotations and in 1000 other comments below, including mine. not sure what else i can do to make people aware of it. if u watch the video, i catch the mistake. thanks tho

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[@patrickjmt]

I make a mistake when I evaluate the third derivative! I write down 2(1/3)^3 but it should be 2(1/2)^3!!!! I catch the mistake but not til the end of the video, so just be aware of that while watching! Sorry for the confusion!!

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[@patrickjmt]

the idea is that a taylor polynomial of degree n approximates the function f(x). suppose that you wanted to use the taylor polynomial to approximate f(2.1)... by centering the taylor polynomial at a=2, your estimate will be closer to the correct value as opposed to say, centering the taylor polynomial at a = 10. basically, the taylor polynomial provides 'good' estimates for those values of x near your a value. so, if you need to calculate f(1000.5), you would use a = 1000 instead of a = 7, etc

[@unknownlove19]

at the third derivative you put (1/3)^3 instead of (1/2)^3 ..thanks for all your vids by the way...you're a life saver.

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[@patrickjmt]

@90sideways well, all the basic laws of newtonian physics can be described as differential equations; power series are a huge way of solving tons of differential equations - so that is one very practical example. also, the 'bell curve' or normal curve in probability uses a function to find areas that can not be integrated using elementary antiderivatives; a power series approximation helps in the area as well. however, i have also not used it yet today in my personal life if that is what u mean

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for the first two years, i put these up 100% for free, with no intent or promise on getting anything in return (this is one of those videos). now the partner program does pay me, but that is certainly not why i started.

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