Lim a* b* x→O XV1_x?
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Lim a* b* x→O XV1_x?

JEE/Engineering Exams
Maths
Solution
119
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( 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)
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