limit as x approaches 0 of x/((4^x-2^x))

解答

x \to 0 lim (\frac{x}{( 4 ^{x} - 2 ^{x} )})

\frac{1}{ln ( 2 )}

十进制

1.44269 \dots

求解步骤

x \to 0 lim (\frac{x}{4 ^{x} - 2 ^{x}})

使用洛必达法则

= x \to 0 lim (\frac{1}{ln ( 2 ) \cdot 2 ^{2 x + 1} - 2 ^{x} ln ( 2 )})

代入值

x = 0

= \frac{1}{ln ( 2 ) \cdot 2 ^{2 \cdot 0 + 1} - 2 ^{0} ln ( 2 )}

化简

\frac{1}{ln ( 2 ) \cdot 2 ^{2 \cdot 0 + 1} - 2 ^{0} ln ( 2 )} : \frac{1}{ln ( 2 )}

= \frac{1}{ln ( 2 )}

\frac{d}{d x} (arcsin (2 x^{5}))

t an g e n t x^{2} + 9

\frac{d}{d x} ((5 x^{3} + 5) (x^{4} - 3 x))

\int [cos (4 x) + cos (8 x)]^{2} d x

\frac{d}{d x} (12 x^{\frac{1}{3}})