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Nice Video Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem That You Share , So Very Nice Thanks You
after i watched this video, my insight is very open because the video is very good to give information Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem
At the end of proof you wrote the last equation which you got using generalized mean value theorem. Can someone explain how can I derive this equality?
@0114mercury Ah, great question. The generalized mean value theorem is used to find an explicit analytic form for the remainder term. We get what is called the Taylor Theorem WITH Remainder. The remainder is a big deal. It is used to confirm (or not) the convergence of the power series. In a rigorous sense the Taylor expansion is useless without the remainder. We have a proof of the GMVT in a previous video: What are Taylor Series? Part 2. Check it out...will add an annotation.
One observation: In elementary Calculus, Taylors Theorem and the Generalized Mean Value Theorem are not always covered but Taylor Series and Taylors Inequality are. It is a simple matter to modify your argument at the very end to produce Taylors Inequality without using the Generalized Mean Value Theorem. This might then be more useful to the typical student. :-)
I am very happy to see the vidoe Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem. from you, hopefully the others also are happy for You
melisantika 1 month ago
I am very happy to see the vidoe after you give this Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem
Onepissite 1 month ago
I Love The Video It Can Increase My Knowledge Taylor's Theorem the Fast and Easy Way.
Ondelendo 1 month ago
Steady I Really Like This Video Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem
bebeheuy 1 month ago
Nice Video Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem That You Share , So Very Nice Thanks You
willamricard 1 month ago
I Really Like The Video From Your Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem
imegatrone 1 month ago
after i watched this video, my insight is very open because the video is very good to give information Mathematics is like mountaineering. Slowly climbing up the mountain to reach the answer or prove the theorem
anakmudajaman 1 month ago
At the end of proof you wrote the last equation which you got using generalized mean value theorem. Can someone explain how can I derive this equality?
Nice proof anyway :-)
0114mercury 6 months ago
@0114mercury Ah, great question. The generalized mean value theorem is used to find an explicit analytic form for the remainder term. We get what is called the Taylor Theorem WITH Remainder. The remainder is a big deal. It is used to confirm (or not) the convergence of the power series. In a rigorous sense the Taylor expansion is useless without the remainder. We have a proof of the GMVT in a previous video: What are Taylor Series? Part 2. Check it out...will add an annotation.
Mathview 6 months ago
Lovely
robkim55 1 year ago
Very nice!
One observation: In elementary Calculus, Taylors Theorem and the Generalized Mean Value Theorem are not always covered but Taylor Series and Taylors Inequality are. It is a simple matter to modify your argument at the very end to produce Taylors Inequality without using the Generalized Mean Value Theorem. This might then be more useful to the typical student. :-)
sdouglas1618 1 year ago
That's a great shortcut but not so obvious.
GR1o6180339887498948 1 year ago