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Anonymous users2024-02-06I don't know if I've learned the upper and lower limits? It is easy to prove with upper and lower limits. Let lim g(x) = positive infinity.
1. When a is a finite number, for any e>0, there is x1, when x>x1, there is a ex1, and a e< [f(x) f(x0)] [g(x) g(x0)] = f'(c)/g'(c) x0.
That is< a e [f(x) g(x) f(x0) g(x)] [1 g(x0) g(x)] a e< = lower limit lim f(x) g(x)< = upper limit lim f(x) g(x)<=a+e, and then let e tend to 0, get.
lim f(x)/g(x)=a=lim f'(x)/g‘(x)。
2. When a is infinite, the condition can be rewritten as lim g'(x)/f'(x)=0, noting that there must be lim f(x)=infinity at this time, so it is proved from the above that there is lim g(x) f(x)=0, so lim f(x) g(x)=positive infinity (note that the numerator and denominator are all positive).
3. When a is negative infinity, consider f(x).
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Anonymous users2024-02-05f(x),g(x) is known as a Taylor series at x=x0, making x close to infinity.
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Anonymous users2024-02-04Personal understanding is wrong, and it must be guided up and down at the same time.
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Anonymous users2024-02-03Your question is a bit vague, but I understand it as two meanings.
The first one: Is it only 0 0 for the type to be used?
For this kind of problem, I would like to illustrate with an example:
lim (e^x)/x
x->o
If you use Lopida's rule, lim (e x x) = (e x).'/x'=(e^x)/1=e^x=e^o=1
x->o
However, this is not the case, first of all, but when x->0, e x=1,1 x-> and 1* - thus.
lim (e^x)/x=∞
x->o
So, only 0 0, this type can be used.
Second: Is it only X->0 or X-> that can be used, can it be used like X->1?
The answer is yes, as long as the numerator and denominator are close to 0 or at x->1, then it will definitely work.
In fact, theorems are absolute, there is no duality, so you don't have to worry about it.
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Anonymous users2024-02-02Hello x 0, sinx x
cosx~1
1-cosx~x²/2
Originalization. lim （e＾x*x-x³-x）/cosx（1-cosx）=lim2（e＾x-x²-1）/x
Use a Robida once.
2lim（e＾x-2x）/1
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Anonymous users2024-02-01<> it's a little messy, but the foot of the lap cong is all in it.
What you said belongs to a set of Western medicine, blood tonic is the specialty of Chinese medicine, and Western medicine is very complicated in this regard, the effect is not necessarily good, you can usually pay more attention to some Chinese medicine blood tonic diet, and anemia depends on food supplement, don't expect medicine to solve these problems......If it is convenient, add a little He Shou Wu or astragalus yam porridge when cooking porridge, and if you take medicine, it is recommended to drink a little ejiao, and you need to pay attention to strengthening the spleen while replenishing blood, so that the nutrients you eat can be absorbed by the body.
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