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標題: [M2] limit revision quesions [打印本頁]

作者: luckjoe    時間: 2021-6-12 02:33 PM     標題: limit revision quesions

Please help to solve the following questions

Thank you very much

Some question I don't why I mixed up the positive and negative signs.
作者: 風之男    時間: 2021-6-12 03:42 PM

As it's a repeated "offense", I urge you to please show your workings and thoughts when asking a math question, no matter how far you get or if it's wrong. Usually you can at least do something by carefully re-reading the question or reviewing what you've learnt. Math is not a spectator sport. Running into dead ends is part of the process, and makes solving a problem eventually even more rewarding.

If you see a limit tending to -infty, use a substitution of y=-x for the very first step to make things easier.

46 should be manageable now.
48 is in a form of "sqrt + sqrt" (well, x is just sqrt(x^2), kind of. Beware of signs). You should know what to do.

For 50, hopefully when you see sine, you are immediately inspired, at some point, to use "limit as A tends to 0 sinA/A = 1". Now where to apply it is not yet apparent (but still you need to know this technique for diff. by first principles).
Here's a well-known enough limit that isn't taught, but I just use it anyway (and state it explicitly when you use it).
"limit as A tends to 0 of (1-cosA)/A = 0"
As to why this is true, multiply and divide (1+cosA) and see what happens.

Solution to 50 in a bit.

EDIT: Solution to 50 -

[ 本帖最後由 風之男 於 2021-6-12 04:22 PM 編輯 ]
作者: luckjoe    時間: 2021-6-13 02:48 PM     標題: 回覆 2# 風之男 的帖子

Thank you very much for your kind assistance.

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