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

解答

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

ln (2)

十进制

0.69314 \dots

求解步骤

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

使用洛必达法则

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

代入值

x = 0

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

化简

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

= ln (2)

\int (sin (x) + 7 cos (x) - 1) d x

\frac{d}{d x} (csc^{3} (x^{2}))

\frac{d}{d x} ((1 + x^{3})^{2020})

s l o p e (8, 8), (4, 6)

d er i v a t i v e e^{2 x} + 2 e^{2 x} x