Question

lim t 0 a^ prime -b^ prime x 3. Evaluate lim​

Answer 1

$\rm{\displaystyle\lim _{x\to \:0}\left(\frac{a^x-b^x}{x}\right)}$

$\rm{\displaystyle=\lim _{x\to \:0}\left(\frac{a^x\ln \left(a\right)-b^x\ln \left(b\right)}{1}\right)}$

$\rm{\displaystyle=\lim _{x\to \:0}\left(a^x\ln \left(a\right)-b^x\ln \left(b\right)\right)}$

$\rm{=a^0\ln \left(a\right)-b^0\ln \left(b\right)}$

$\rm{=\ln \left(a\right)-\ln \left(b\right)}$