What is the limit as x approaches 0 of ((4^x-1))/x ?

The limit as x approaches 0 of ((4^x-1))/x is 2ln(2)

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limit as x approaches 0 of ((4^x-1))/x

x \to 0 lim (\frac{( 4 ^{x} - 1 )}{x})

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

x \to 0 lim (\frac{4 ^{x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1})

= x \to 0 lim (\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1})

Plug in the value

x = 0

= \frac{ln ( 2 ) \cdot 2 ^{2 \cdot 0 + 1}}{1}

Simplify

= 2 ln (2)

\int sin (7 x - 10) d x

x \to \infty lim (4 x^{3})

\frac{d}{d x} (12 x^{3})

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))

\frac{d}{d x} (\frac{4}{9} x^{3})

What is the limit as x approaches 0 of ((4^x-1))/x ?
The limit as x approaches 0 of ((4^x-1))/x is 2ln(2)