Taylor's Theorem with Remainder

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This videos shows how to determine the error when approximating a function value with a Taylor polynomial.

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Your videos are awesome. I can't make any sense of what my instructor teaches us in a two hour lecture, but I can watch your 9 minute lecture and understand it completely.

erikholgersen

I just realized that these videos are like 11 years old now but it helps me a lot more than any other videos these days. Thank you a lot for the video 💕

hannahahn

watched many YouTube videos on this topic, this is the one that helped things sink in... thank you

DebaucherousDaniels

you did the first example wrong... the max on the interval is not 1 because your interval is (0, .1) therefore, your max would be sin(.1).. so the R4(x) is actually 8.319 * 10^-9

swimchic

Thank You for your hard word, in my opinion I think you're the best calc. instructor on youtube.. <3

faisaladnan

Question: why do you use 2 instead of e^0.5 ?
will e^0.5 give a wrong answer? when I uses e^0.5 i got 0.0043 as final answer

julebrus

Thank you much for making this video! i was having such a hard time understanding this and you made it so much clearer. Have a wonderful life and thanks for taking the time to help others!

maxfsbb

Best taylor's theorem explanation on youtube

natalien

you sir have solved chapter 9 for me! thank you! thank you! thank you!

onice

for the second problem... why is the error less than or equal to and not just "less than" 2/4!(.5)^4 ? If we proved that e^.5< 2 then shouldn't the remainder also just be less than?

shadowobito

Was the interval for k given or you chose it yourself?

romeodaniels

how do we know that k is the range [ 0, 0.5 ]

SarahRuscoe

If you had a function such as arccos(x) and you needed to estimate arccos(0.3), how would you find the max value?

janessaschwallie

The limit as n approaches infinity for the Taylor Series would be the same as if you would just perform the function. It is meant to be an easy approximation not the actual value, which can be difficult to solve sometimes.

Veggiepunch

in the first example of cos(0, 1), if k can be -1<=k<=1 to get the max, how is that consistent with the definition of k being between c=0 and x=0, 1???

thanks for answer!

Daski

Thank you. This simple explanation helped me make sense of my textbook. Great work!

richardslabbert

Very good quality videos. Thank you for making things so clear. Isn't the remainder the remaining terms up to infinity? I am puzzled that you (or Taylor) are taking only the next term in the series and saying this is the remainder.

leonig

Odd Eirik Hardem: With access to a caluculator I agree, there is little point in saying that e^0.5 can max be 2 (note that it is still correct though), but in an exam with no GDC allowed this trick comes in handy.

jonathanhole

cant we just use the limit as n--> infinity of (x ^ n )/ n! = 0? then 0 times anything will be zero, , so at last, we can conclude that f(x) = Tn(x) - 0

correct me if i am wrong ; )

AndyGor

Your videos are awesome. You should be a prof. at Yale.

AnAboveAverageGolfer

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