What is the limit as x approaches 1 of (2^x-2)/(x-1) ?

The limit as x approaches 1 of (2^x-2)/(x-1) is 2ln(2)

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limit as x approaches 1 of (2^x-2)/(x-1)

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

2 ln (2)

Decimal

1.38629 \dots

Solution steps

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

Apply L'Hopital's Rule

= x \to 1 lim (\frac{ln ( 2 ) \cdot 2 ^{x}}{1})

Plug in the value

x = 1

= \frac{ln ( 2 ) \cdot 2 ^{1}}{1}

Simplify

= 2 ln (2)

What is the limit as x approaches 1 of (2^x-2)/(x-1) ?
The limit as x approaches 1 of (2^x-2)/(x-1) is 2ln(2)