What is the limit as x approaches 0 of (6^x-7^x)/x ?

The limit as x approaches 0 of (6^x-7^x)/x is ln(6)-ln(7)

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limit as x approaches 0 of (6^x-7^x)/x

x \to 0 lim (\frac{6 ^{x} - 7 ^{x}}{x})

ln (6) - ln (7)

Decimal

- 0.15415 \dots

Solution steps

x \to 0 lim (\frac{6 ^{x} - 7 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 7 ^{x} ln ( 7 )}{1})

= x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 7 ^{x} ln ( 7 )}{1})

Plug in the value

x = 0

= \frac{6 ^{0} ln ( 6 ) - 7 ^{0} ln ( 7 )}{1}

Simplify

\frac{6 ^{0} ln ( 6 ) - 7 ^{0} ln ( 7 )}{1} : ln (6) - ln (7)

= ln (6) - ln (7)

\frac{d}{d x} (e^{- x} \cdot sin^{2} (x))

10 \cdot \frac{1}{1 + 6 s}

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\frac{\partial}{\partial x} (5 x - y + 7 x y)

What is the limit as x approaches 0 of (6^x-7^x)/x ?
The limit as x approaches 0 of (6^x-7^x)/x is ln(6)-ln(7)