A problem on the limit of higher numbers It is known that f (x) is continuous when x = 0, then if Lim [f (x) / x] exists (under the condition of X - > 0), then f (0) = 0, why?

A problem on the limit of higher numbers It is known that f (x) is continuous when x = 0, then if Lim [f (x) / x] exists (under the condition of X - > 0), then f (0) = 0, why?

Counter evidence
Suppose f (x) is not equal to zero, then Lim [f (x) / x] = infinite, that is, the limit does not exist, contradictory, so f (0) = 0, you can talk online if you don't understand

Elden Ring Premiere

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