What is the limit as x approaches 0 of (11^x-10^x)/x ?

The limit as x approaches 0 of (11^x-10^x)/x is ln(11)-ln(10)

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limit as x approaches 0 of (11^x-10^x)/x

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

ln (11) - ln (10)

Decimal

0.09531 \dots

Solution steps

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

Apply L'Hopital's Rule

= x \to 0 lim (\frac{1 1 ^{x} ln ( 11 ) - 1 0 ^{x} ln ( 10 )}{1})

Plug in the value

x = 0

= \frac{1 1 ^{0} ln ( 11 ) - 1 0 ^{0} ln ( 10 )}{1}

Simplify

\frac{1 1 ^{0} ln ( 11 ) - 1 0 ^{0} ln ( 10 )}{1} : ln (11) - ln (10)

= ln (11) - ln (10)

d er i v a t i v e G (t) = \frac{4 t}{t + 5}

\frac{d}{d x} (arcsin (3 x - 4 x^{3}))

d er i v a t i v e lo g_{3} (11) p^{3}

t an g e n t y = \frac{5}{x}, (1, 5)

\frac{d}{d x} (\frac{sin ( 2 x )}{1 + cos ( x )})

What is the limit as x approaches 0 of (11^x-10^x)/x ?
The limit as x approaches 0 of (11^x-10^x)/x is ln(11)-ln(10)