What is the limit as x approaches 0 of (1^x-9^x)/x ?

The limit as x approaches 0 of (1^x-9^x)/x is -2ln(3)

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limit as x approaches 0 of (1^x-9^x)/x

x \to 0 lim (\frac{1 ^{x} - 9 ^{x}}{x})

- 2 ln (3)

Decimal Notation

- 2.19722 \dots

Solution steps

x \to 0 lim (\frac{1 ^{x} - 9 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 2 ln ( 3 ) \cdot 9 ^{x}}{1})

= x \to 0 lim (\frac{- 2 ln ( 3 ) \cdot 9 ^{x}}{1})

Plug in the value

x = 0

= \frac{- 2 ln ( 3 ) \cdot 9 ^{0}}{1}

Simplify

= - 2 ln (3)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} - x^{2} y)

\int \frac{10}{1 - x ^{2}} d x

x y^{^{''}} - 2 y^{^{'}} = 0

\int \frac{6}{( 9 t ^{2} + 1 ) ^{2}} d t

\frac{d}{d x} (A x^{2} e^{x})

What is the limit as x approaches 0 of (1^x-9^x)/x ?
The limit as x approaches 0 of (1^x-9^x)/x is -2ln(3)