What is the limit as x approaches 0 of (21^x-1)/x ?

The limit as x approaches 0 of (21^x-1)/x is ln(21)

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limit as x approaches 0 of (21^x-1)/x

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

ln (21)

Decimal Notation

3.04452 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{ln ( 21 ) \cdot 2 1 ^{x}}{1})

= x \to 0 lim (\frac{ln ( 21 ) \cdot 2 1 ^{x}}{1})

Plug in the value

x = 0

= \frac{ln ( 21 ) \cdot 2 1 ^{0}}{1}

Simplify

= ln (21)

\int \frac{1}{2 x ( 1 + x )} d x

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}

f (x) = x^{2} + 2, at x = 3

\frac{d}{d x} (4 x arcsin (x))

\frac{d}{d x} (\frac{ln ( 1 )}{x})

What is the limit as x approaches 0 of (21^x-1)/x ?
The limit as x approaches 0 of (21^x-1)/x is ln(21)