What is the limit as x approaches 0 of (2.8^x-1)/x ?

The limit as x approaches 0 of (2.8^x-1)/x is 1.02961…

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limit as x approaches 0 of (2.8^x-1)/x

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

1.02961 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1.02961 \dots \cdot 2. 8 ^{x}}{1})

= x \to 0 lim (\frac{1.02961 \dots \cdot 2. 8 ^{x}}{1})

Plug in the value

x = 0

= \frac{1.02961 \dots \cdot 2. 8 ^{0}}{1}

Simplify

= 1.02961 \dots

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What is the limit as x approaches 0 of (2.8^x-1)/x ?
The limit as x approaches 0 of (2.8^x-1)/x is 1.02961…