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})

= 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

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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…