What is the limit as x approaches 0 of (3^x-11^x)/x ?

The limit as x approaches 0 of (3^x-11^x)/x is ln(3)-ln(11)

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limit as x approaches 0 of (3^x-11^x)/x

x \to 0 lim (\frac{3 ^{x} - 1 1 ^{x}}{x})

ln (3) - ln (11)

Decimal

- 1.29928 \dots

Solution steps

x \to 0 lim (\frac{3 ^{x} - 1 1 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 1 1 ^{x} ln ( 11 )}{1})

= x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 1 1 ^{x} ln ( 11 )}{1})

Plug in the value

x = 0

= \frac{3 ^{0} ln ( 3 ) - 1 1 ^{0} ln ( 11 )}{1}

Simplify

\frac{3 ^{0} ln ( 3 ) - 1 1 ^{0} ln ( 11 )}{1} : ln (3) - ln (11)

= ln (3) - ln (11)

x \to 3 + lim (sec (\frac{π x}{6}))

\int \frac{( x - 2 ) ( x + 3 )}{x ^{2}} d x

\frac{d}{d x} (72 cos (x))

(2 x + y) d x + (x + 6 y) d y = 0

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

What is the limit as x approaches 0 of (3^x-11^x)/x ?
The limit as x approaches 0 of (3^x-11^x)/x is ln(3)-ln(11)