What is the limit as x approaches 0 of (2.7^x-1)/x ?

The limit as x approaches 0 of (2.7^x-1)/x is 0.99325…

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limit as x approaches 0 of (2.7^x-1)/x

x \to 0 lim (\frac{2. 7 ^{x} - 1}{x})

0.99325 \dots

Solution steps

x \to 0 lim (\frac{2. 7 ^{x} - 1}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{0.99325 \dots \cdot 2. 7 ^{x}}{1})

Plug in the value

x = 0

= \frac{0.99325 \dots \cdot 2. 7 ^{0}}{1}

Simplify

= 0.99325 \dots

\frac{d}{d x} (3 x^{2} + 4 x - 5)

t a y l or e^{x} - 1

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

\frac{\partial}{\partial x} (x^{3} + 2 x y - y^{2})

d er i v a t i v e y = \frac{3}{4 x ^{5}}

What is the limit as x approaches 0 of (2.7^x-1)/x ?
The limit as x approaches 0 of (2.7^x-1)/x is 0.99325…