limit as x approaches 0 of (9^x-13^x)/x

解答

x \to 0 lim (\frac{9 ^{x} - 1 3 ^{x}}{x})

2 ln (3) - ln (13)

十进制

- 0.36772 \dots

求解步骤

x \to 0 lim (\frac{9 ^{x} - 1 3 ^{x}}{x})

使用洛必达法则

= x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x} - 1 3 ^{x} ln ( 13 )}{1})

代入值

x = 0

= \frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 3 ^{0} ln ( 13 )}{1}

化简

\frac{2 ln ( 3 ) \cdot 9 ^{0} - 1 3 ^{0} ln ( 13 )}{1} : 2 ln (3) - ln (13)

= 2 ln (3) - ln (13)

t an g e n t (8 x - x^{2}) (1.7)

\frac{d}{d x} ((x^{3} + 2 x + 6) (4 + \frac{1}{x ^{2}}))

\int_{0}^{\infty} e^{- 5 x} d x

\int \frac{- x - 1}{x} d x

d er i v a t i v e (1 + e^{- t})^{- 1} + e^{- 1}