de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

limit as x approaches 1+of 3/(ln(x))-2/(x-1)

Lösung

x \to 1 + lim (\frac{3}{ln ( x )} - \frac{2}{x - 1})

Lösung

\infty

Schritte zur Lösung

x \to 1 + lim (\frac{3}{ln ( x )} - \frac{2}{x - 1})

Vereinfache

\frac{3}{ln ( x )} - \frac{2}{x - 1} : \frac{3 ( x - 1 ) - 2 ln ( x )}{ln ( x ) ( x - 1 )}

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

Wende das L'Hopital Theorem an

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

Vereinfache

\frac{3 - \frac{2}{x}}{\frac{x - 1}{x} + ln ( x )} : \frac{3 x - 2}{x - 1 + x ln ( x )}

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

\frac{3 x - 2}{x - 1 + x ln ( x )} = (3 x - 2) \frac{1}{x - 1 + x ln ( x )}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= x \to 1 + lim (3 x - 2) \cdot x \to 1 + lim (\frac{1}{x - 1 + x ln ( x )})

x \to 1 + lim (3 x - 2) = 1

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

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

Graph

Beliebte Beispiele

tangent y= 4/x ,(5, 4/5)

t an g e n t y = \frac{4}{x}, (5, \frac{4}{5})

derivative (ln(7x))^2

d er i v a t i v e (ln (7 x))^{2}

(\partial)/(\partial x)(2^{-x})

\frac{\partial}{\partial x} (2^{- x})

integral of 8/((t^2+1)^{3/2)}

\int \frac{8}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

integral from-2 to 1 of x^3

\int_{- 2}^{1} x^{3} d x