What is the limit as x approaches 0 of (10^x-1)/x ?

The limit as x approaches 0 of (10^x-1)/x is ln(10)

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limit as x approaches 0 of (10^x-1)/x

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

ln (10)

Decimal Notation

2.30258 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{ln ( 10 ) \cdot 1 0 ^{x}}{1})

= x \to 0 lim (\frac{ln ( 10 ) \cdot 1 0 ^{x}}{1})

Plug in the value

x = 0

= \frac{ln ( 10 ) \cdot 1 0 ^{0}}{1}

Simplify

= ln (10)

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f (x) = 2 x^{4} - 11 x^{2}, at x = 1

\int \frac{x}{2 x ^{2} + 3} d x

What is the limit as x approaches 0 of (10^x-1)/x ?
The limit as x approaches 0 of (10^x-1)/x is ln(10)