limit as x approaches 1 of (3x)/(x-1)-3/(ln(x))

解答

x \to 1 lim (\frac{3 x}{x - 1} - \frac{3}{ln ( x )})

\frac{3}{2}

十进制

1.5

求解步骤

x \to 1 lim (\frac{3 x}{x - 1} - \frac{3}{ln ( x )})

化简

\frac{3 x}{x - 1} - \frac{3}{ln ( x )} : \frac{3 x ln ( x ) - 3 ( x - 1 )}{ln ( x ) ( x - 1 )}

= x \to 1 lim (\frac{3 x ln ( x ) - 3 ( x - 1 )}{ln ( x ) ( x - 1 )})

使用洛必达法则

= x \to 1 lim (\frac{3 ln ( x )}{\frac{x - 1}{x} + ln ( x )})

使用洛必达法则

= x \to 1 lim (\frac{\frac{3}{x}}{\frac{1}{x ^{2}} + \frac{1}{x}})

代入值

x = 1

= \frac{\frac{3}{1}}{\frac{1}{1 ^{2}} + \frac{1}{1}}

化简

\frac{\frac{3}{1}}{\frac{1}{1 ^{2}} + \frac{1}{1}} : \frac{3}{2}

= \frac{3}{2}

\frac{d}{d x} (\frac{sin ( 6 x )}{e ^{3 x}})

d er i v a t i v e f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

\frac{1}{3} \frac{d x}{d t} - 2 e^{- t} = - x

\int_{l n (8)}^{l n (64)} e^{\frac{x}{3}} d x

x \to 0 + lim (x - x)