I tried to recall the standard proof of [MATH]\lim_{x \to 0} \frac{e^x-1}{x}=1[/MATH] but then I got an idea and did this:
[MATH]\lim_{x \to 0} \frac{e^x-1}{x}=\lim_{x \to 0} \frac{((1+x)^{1/x})^x-1}{x}=\lim_{x \to 0} \frac{1+x-1}{x}=1[/MATH]I just wanted to check if it's valid to prove it this way. Thanks a lot!
[MATH]\lim_{x \to 0} \frac{e^x-1}{x}=\lim_{x \to 0} \frac{((1+x)^{1/x})^x-1}{x}=\lim_{x \to 0} \frac{1+x-1}{x}=1[/MATH]I just wanted to check if it's valid to prove it this way. Thanks a lot!