Exponential and logarithmic standard limits for JEE

Formula

\[\lim_{x\to 0}\frac{e^x-1}{x}=1,\qquad \lim_{x\to 0}\frac{a^x-1}{x}=\ln a,\qquad \lim_{x\to 0}\frac{\ln(1+x)}{x}=1\]

Variables: \(a>0,a\neq 1\).

Conditions: For real logarithm, \(1+x>0\) near \(0\).

Limits, derivatives of exponential/logarithmic functions.