What is the limit as x approaches 0 of (8e^{2x}-8)/(e^x-1) ?

The limit as x approaches 0 of (8e^{2x}-8)/(e^x-1) is 16

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limit as x approaches 0 of (8e^{2x}-8)/(e^x-1)

x \to 0 lim (\frac{8 e ^{2 x} - 8}{e ^{x} - 1})

16

Solution steps

x \to 0 lim (\frac{8 e ^{2 x} - 8}{e ^{x} - 1})

Simplify

\frac{8 e ^{2 x} - 8}{e ^{x} - 1} : 8 (e^{x} + 1)

= x \to 0 lim (8 (e^{x} + 1))

Plug in the value

x = 0

= 8 (e^{0} + 1)

Simplify

= 16

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

x \to 0 lim (x sin (\frac{e}{x}))

x \to 0 lim (\frac{∣ x ∣ sin ( x )}{x})

t \to 0 + lim (ln (tan (t)))

x \to 2 lim (8 x - 5)

What is the limit as x approaches 0 of (8e^{2x}-8)/(e^x-1) ?
The limit as x approaches 0 of (8e^{2x}-8)/(e^x-1) is 16