Lim_x → 0a^x a^ x/x = lim_x → 0(a^x 1) (a^ x 1)/x = lim_x → 0a^x 1/xlim_x → 0a^x 1/x = lim_x → 0a^x 1/x + lim_x → 0a^ x 1/( x) = log a + log a = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Standard Limits to Remove Indeterminate Form

lim x → 0ax-a...

Question

${lim}_{x \to 0} \frac{a^{x} - a^{- x}}{x}$

Open in App

Solution

${lim}_{x \to 0} \frac{a^{x} - a^{- x}}{x} = {lim}_{x \to 0} \frac{(a^{x} - 1) - (a^{- x} - 1)}{x} = {lim}_{x \to 0} \frac{a^{x} - 1}{x} {lim}_{x \to 0} \frac{a^{x} - 1}{x} = {lim}_{x \to 0} \frac{a^{x} - 1}{x} + {lim}_{x \to 0} \frac{a^{- x} - 1}{(- x)} = log a + log a = 2 {log}_{e} 2$

Suggest Corrections

Similar questions

\lim_{x \to 0} \frac{a^{x} + a^{- x} - 2}{x^{2}}

lim x \to 0 \frac{a^{x} - b^{x}}{x}

${lim}_{x \to 0} \frac{a^{x} + a^{- x} - 2}{x^{2}}$

${lim}_{x \to 0} \frac{a^{x} + b^{x} - 2}{x}$

${lim}_{x \to 0} \frac{a^{x} + b^{x} - c^{x} - d^{x}}{x}$

Join BYJU'S Learning Program