Sunday, October 11, 2015

calculus - Find $lim_{x to 0^{+}} frac{ln(x+1)}{x}$ without using L'Hopital's Rule?

Without using L'Hopital's Rule, how does one find $\lim_{x \to 0^{+}} \frac{\ln(x+1)}{x}$?



I was hoping to find a way using basic calc I, pre-differentiation knowledge and not knowing the definition of $e$--much like you can prove $\lim_{x\to\infty} \frac{\sin x}{x} = 1$ using a geometric argument and the squeeze rule/theorem.

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