limit as x approaches 0 of ((ln(1+x)))/x

解答

x \to 0 lim (\frac{( ln ( 1 + x ) )}{x})

1

求解步骤

x \to 0 lim (\frac{ln ( 1 + x )}{x})

\frac{ln ( 1 + x )}{x} = ln (1 + x) \frac{1}{x}

= x \to 0 lim (ln (1 + x) \frac{1}{x})

化简

ln (1 + x) \frac{1}{x} : \frac{ln ( 1 + x )}{x}

= x \to 0 lim (\frac{ln ( 1 + x )}{x})

使用洛必达法则

= x \to 0 lim (\frac{\frac{1}{1 + x}}{1})

代入值

x = 0

= \frac{\frac{1}{1 + 0}}{1}

化简

= 1

\int (3 x - 2)^{4} d x

t a y l or x^{2}, 0

d er i v a t i v e f (x) = \frac{( 1 - 4 x )}{1 + 4 x}

\int \frac{ln ( 2 x )}{x ln ( x )} d x

x \to 1 lim (\frac{1 - x ^{2}}{x - 1})