What is the limit as t approaches 0 of (5^t-1)/t ?

The limit as t approaches 0 of (5^t-1)/t is ln(5)

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limit as t approaches 0 of (5^t-1)/t

t \to 0 lim (\frac{5 ^{t} - 1}{t})

ln (5)

Decimal

1.60943 \dots

Solution steps

t \to 0 lim (\frac{5 ^{t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{ln ( 5 ) \cdot 5 ^{t}}{1})

= t \to 0 lim (\frac{ln ( 5 ) \cdot 5 ^{t}}{1})

Plug in the value

t = 0

= \frac{ln ( 5 ) \cdot 5 ^{0}}{1}

Simplify

= ln (5)

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

x \to 4 lim ([\frac{x ^{2} + 4}{5}])

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

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

x \to 2 lim (5 x + 9)

What is the limit as t approaches 0 of (5^t-1)/t ?
The limit as t approaches 0 of (5^t-1)/t is ln(5)