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

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

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

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

2

Solution steps

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

f (t) = sin^{2} (t)

x \to 3 lim (\frac{x ^{2} + x}{x + 3})

\int \frac{13}{x ^{2} - 1} d x

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

\int \frac{9 - x ^{2}}{5 x ^{3} + x} d x

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