What is the limit as t approaches 0 of ((3e^t-3))/t ?

The limit as t approaches 0 of ((3e^t-3))/t is 3

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limit as t approaches 0 of ((3e^t-3))/t

t \to 0 lim (\frac{( 3 e ^{t} - 3 )}{t})

3

Solution steps

t \to 0 lim (\frac{3 e ^{t} - 3}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{3 e ^{t}}{1})

= t \to 0 lim (\frac{3 e ^{t}}{1})

Plug in the value

t = 0

= \frac{3 e ^{0}}{1}

Simplify

= 3

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

x \to 0 + lim (\frac{8 x}{sin ( x )})

x \to - 3 lim (∣ x + 3 ∣)

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

(\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) (y + 4 y^{3})

What is the limit as t approaches 0 of ((3e^t-3))/t ?
The limit as t approaches 0 of ((3e^t-3))/t is 3