What is the limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x) ?

The limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x) is 2

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limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x)

x \to 0 lim (\frac{e ^{4 x} - 1}{2 x ^{2} + 2 x})

2

Solution steps

x \to 0 lim (\frac{e ^{4 x} - 1}{2 x ^{2} + 2 x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{4 e ^{4 x}}{4 x + 2})

Plug in the value

x = 0

= \frac{4 e ^{4 \cdot 0}}{4 \cdot 0 + 2}

Simplify

\frac{4 e ^{4 \cdot 0}}{4 \cdot 0 + 2} : 2

= 2

What is the limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x) ?
The limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x) is 2