limit as x approaches 2 of (4ln(2x-3))/(2e^{2x-4)-2}

Lösung

x \to 2 lim (\frac{4 ln ( 2 x - 3 )}{2 e ^{2 x - 4} - 2})

2

Schritte zur Lösung

x \to 2 lim (\frac{4 ln ( 2 x - 3 )}{2 e ^{2 x - 4} - 2})

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

= 4 \cdot x \to 2 lim (\frac{ln ( 2 x - 3 )}{2 e ^{2 x - 4} - 2})

Wende das L'Hopital Theorem an

= 4 \cdot x \to 2 lim (\frac{\frac{2}{2 x - 3}}{4 e ^{2 x - 4}})

Setze den Wert

x = 2

ein

= 4 \cdot \frac{\frac{2}{2 \cdot 2 - 3}}{4 e ^{2 \cdot 2 - 4}}

Vereinfache

4 \cdot \frac{\frac{2}{2 \cdot 2 - 3}}{4 e ^{2 \cdot 2 - 4}} : 2

= 2

x \to b lim (\frac{b - x}{x - b})

x \to 1 lim (3 x + 2)

x \to 1 lim (3 x^{2} - 7 x + 2)

x \to 0 lim ((2^{x} + x)^{\frac{1}{x}})

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