What is the limit as x approaches 0 of (e^x-2^x)/x ?

The limit as x approaches 0 of (e^x-2^x)/x is 1-ln(2)

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limit as x approaches 0 of (e^x-2^x)/x

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

1 - ln (2)

Decimal

0.30685 \dots

Solution steps

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

Apply L'Hopital's Rule

= x \to 0 lim (\frac{e ^{x} - 2 ^{x} ln ( 2 )}{1})

Plug in the value

x = 0

= \frac{e ^{0} - 2 ^{0} ln ( 2 )}{1}

Simplify

= 1 - ln (2)

What is the limit as x approaches 0 of (e^x-2^x)/x ?
The limit as x approaches 0 of (e^x-2^x)/x is 1-ln(2)