What is the limit as t approaches 0 of (sin(5t))/t ?

The limit as t approaches 0 of (sin(5t))/t is 5

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 (sin(5t))/t

t \to 0 lim (\frac{sin ( 5 t )}{t})

5

Solution steps

t \to 0 lim (\frac{sin ( 5 t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{cos ( 5 t ) \cdot 5}{1})

= t \to 0 lim (\frac{cos ( 5 t ) \cdot 5}{1})

Plug in the value

t = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{cos ( 5 \cdot 0 ) \cdot 5}{1} : 5

= 5

x \to \infty lim (x^{- a})

x \to - 4 lim (250)

x \to 0 + lim (\frac{x}{x ^{2}})

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

x \to 1 lim (2 + 2)

What is the limit as t approaches 0 of (sin(5t))/t ?
The limit as t approaches 0 of (sin(5t))/t is 5