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

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

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

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

ln (7) - ln (6)

Decimal

0.15415 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= ln (7) - ln (6)

x \to 0 lim ((4 x + 1)^{\frac{1}{x}})

x \to 2 - lim (\frac{x - 1}{x ^{2} - 4})

x \to 0 lim (x [x] cot (x))

b \to \infty lim (e^{- b})

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

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