What is the limit as t approaches 0 of (e^{2t}-1)/t ?

The limit as t approaches 0 of (e^{2t}-1)/t is 2

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limit as t approaches 0 of (e^{2t}-1)/t

t \to 0 lim (\frac{e ^{2 t} - 1}{t})

2

Solution steps

t \to 0 lim (\frac{e ^{2 t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{2 e ^{2 t}}{1})

= t \to 0 lim (\frac{2 e ^{2 t}}{1})

Plug in the value

t = 0

= \frac{2 e ^{2 \cdot 0}}{1}

Simplify

= 2

y = ln (30) + 3 0^{x + 4}

x \to 4 lim (x^{2} - 16)

\int 3 x - 8 d x

\frac{\partial ^{2}}{\partial y ^{2}} (x^{2} - y^{2})

What is the limit as t approaches 0 of (e^{2t}-1)/t ?
The limit as t approaches 0 of (e^{2t}-1)/t is 2