Definition of Derivatives to Prove limit ln(1 + x)/x = 1

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Hi! I somehow cannot understand why lim as x->0 f(x)/x = lim as x->0 (f(x)-f(0))/x-0. ( minute 1:38 ) Can you help me understand?

gabriardi
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I really like your problems could you please say where did you get those questions or which book ?

fnda
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So this upload is almost a year old?
First question;
what is there to know/notice about the definition of derivative that tells you to first find the derivative of the numerator (of the original function)?

coreys
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how do is prove this when x has to be > 0 ?

KarmaGeeGee