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

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

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

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

2

Solution steps

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})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 2

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

Simplify

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

= 2

x \to 0 lim (x^{2} sec^{2} (x))

x \to \infty lim (3 x e^{x})

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

y \to 1 lim (\frac{y ^{11} + 2 y - 3}{y ^{7} + y ^{2} - y - 1})

x \to 1 lim (3 x + 2)

What is the limit as x approaches 2 of (4ln(2x-3))/(2e^{2x-4)-2} ?
The limit as x approaches 2 of (4ln(2x-3))/(2e^{2x-4)-2} is 2