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

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

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

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

e

Decimal Notation

2.71828 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{e ^{0 + 1}}{1}

Simplify

= e

x \to 2 lim (\frac{x - 2}{4 - 2 x})

x \to 0 lim (\frac{x ^{2} - 9}{x})

x \to \infty lim (x^{4} - 4 x)

x \to - 3 lim (x^{4} + 2 x^{2} + 3 x - 3)

x \to 8 lim (4)

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