Calculus: Advanced topic: Proving Limit Rules

[brob345]

however, could you please prove that lim(1/g) = 1/M

[brob345]

this made my intro to analysis life a little bit easier, thanks @ProfessorElvisZap , and I appreciate the sinister trick face at 3:03 , its funny, but I finally understood why epsilon/2 is used

[cuntbench]

@brob345 is this because we are finding the limit of the sum of two functions? if we were to find the limit of 3 would it be epsilon/3?

[offfaceoff]

brutal lecturer. typical of a prof that knows the topic inside out but cannot convey to those at early stage of learning

[TheNiggerXavi]

mathematical rigour -.-

[Lebedis66]

When prooving limit product rule, why didn't you ensure that m, l in the denominator are not zero ? Otherwise, shouldn't you consider the cases when one of the limit is zero ? It seems that this proof is false for l,m=0...

[ProfessorElvisZap]

@Lebedis66 TrueDat, but if either M on L is 0 then the result follows more easily.

[Lebedis66]

When prooving limit product rule, why didn't you ensure that m, l in the denominator are not zero ? Otherwise, shouldn't you consider the cases when one of the limit is zero ?

[ProfessorElvisZap]

@nukedragon For ANY epsilon, you can find an appropriate delta. Because I know that there are two terms in the sum rule, I adjust each delta to work for epsilon/2, then the sum is smaller than 2(epsilon/2) = epsilon. It is a little like planning a construction project. If you have to tile a floor, you plan for about 5% waste. So if the floor is 100 square feet you buy 105 square feet of tile. In a similar fashion, I know I need to make things < epsilon. So I plan ahead with epsilon/2.

[nukedragon]

In the proof of the addition of limits, at the nasty trick part, where did epsilon over 2 come from? I have seen it before but I don't know how you came up with that. Please help me, thanx.

[trumpetplayer231]

are u a professer?

[ProfessorElvisZap]

This video is not a beginner topic. There are a couple of steps that are skipped --- namely that each of the deltas are chosen in the last step so that everything works out. These ideas will be easier once you read through the definition of a limit, and you attempt to follow the proof.

[nacho862]

@ProfessorElvisZap I like the video, the first proof is reminiscent of something a proof we used to do in multivariable calculus. I'm taking my first course in advanced calculus next year and was wondering if there are interesting resources (besides your vids of course) concerning advanced calculus. I feel like I don't have enough experience proving things in calculus (used to algebra, more so).

[ProfessorElvisZap]

@nacho862 The proofs I gave were lovingly lifted from Rudin's "Principles of Mathematical Analysis." This is a must read for math majors, but it may be the first book in which you struggle to understand. When i learned from it, I literally memorized the statements, definitions, and proofs, until the ideas were comfortable.

Also, Spivak's calculus book is nice. There are newer resources available in the American Math Society's catalogue that are worth looking into. Good luck!

[summdy1]

ahw... can you make it more easier?? I was not yet able to attend a formal class of calculus.. make it understandable for beginners in calculus.. thank you