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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

1

Solution steps

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

Simplify

\frac{2}{t} - \frac{2}{e ^{t} - 1} : \frac{2 ( e ^{t} - 1 ) - 2 t}{t ( e ^{t} - 1 )}

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

\frac{2 e ^{0}}{e ^{0} \cdot 0 + 2 e ^{0}} : 1

= 1

\frac{d}{d x} ((x^{8} - 1)^{3})

\int cot^{2} (x cs) c^{4} x d x

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

\frac{d}{d x} (\frac{cos ( y ) + 2 e ^{- x} cos ( x )}{y})

y = 3 x e^{x}, (0, 0)

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