What is the limit as t approaches 0 of (ln(2t+1))/t ?

The limit as t approaches 0 of (ln(2t+1))/t is 2

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 (ln(2t+1))/t

t \to 0 lim (\frac{ln ( 2 t + 1 )}{t})

2

Solution steps

t \to 0 lim (\frac{ln ( 2 t + 1 )}{t})

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

= \frac{\frac{2}{2 \cdot 0 + 1}}{1}

Simplify

= 2

x \to - 5 lim (sin (\frac{π}{3} x))

x \to - 1 lim (2 x + 7)

x \to 7 + lim (\frac{x - 8}{x - 7})

x \to 6 lim (- x^{2} + 6 x)

x \to 3 lim (3 - 7 x - 5 x^{2})

What is the limit as t approaches 0 of (ln(2t+1))/t ?
The limit as t approaches 0 of (ln(2t+1))/t is 2