Question
( lim _{x rightarrow 0} frac{a^{x}-b^{x}}{x sqrt{1-x^{2}}} )
( left(frac{0}{0} text { form - Apply } 1 text { - Hopital s rule }right] ) ( lim _{x rightarrow 0} frac{a^{x} log a-b^{x} log b}{sqrt{1-x^{2}}+x frac{(-2 x)}{2 sqrt{1-x^{2}}}} )
( lim _{x rightarrow 0} frac{left(a^{x} log a-b^{x} log bright) sqrt{1-x^{2}}}{1-x^{2}-x^{2}} )
( frac{left(a^{0} log a-b^{0} log bright) sqrt{1-0}}{1-0} )
( log a-log b )
( log left(frac{a}{b}right)

Lim a* b* x→O XV1_x?
Solution
