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The limit of absolute value As follows: lim│x│ ( x→0)
The left and right limits are calculated separately
Left limit: from the negative direction close to 0, get: Lim | x | = - limx = 0
Right limit: from the positive direction close to 0, get: Lim | x | = limx = 0
Left limit = right limit
So the limit is 0
Is there any relationship between the absolute value of limit and the limit of absolute value?
The absolute value of limit is simple. It is possible to find the limit first and then the absolute value. The limit of absolute value is complex. Depending on the specific situation, it is generally necessary to discuss the existence of limit. From the direction of x0 + and x0 - respectively, we can see whether they all exist and whether they are equal
The problem of absolute value limit
The absolute value of the function g (x) = | 2x | (2x) is known. Ask if the limit of [g (0 + H) - G (0)] / h exists when h approaches 0. Please give the process and reason of the solution
Personally, I don't think it exists
Firstly, when x > = 0, G (x) = 2x. When x0, it can be expanded as: (2h-0) / h = 2H / h = 2
The limit at H0 does not exist. However, if we only consider such intervals as (0, positive infinity) or (negative infinity, 0), then the limit exists. According to the analysis just now, we can get 2 and - 2 respectively
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