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

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

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

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

5

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

= \frac{5 e ^{0}}{1}

Simplify

= 5

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\frac{d}{d x} (ln (\frac{7}{x ^{2} - x + 2}))

y^{^{''}} - 8 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = 5

\int_{- \infty}^{0} x e^{9 x} d x

\frac{\partial}{\partial y} (y^{3} - y)

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