What is the limit as x approaches 0 of 8xcsc(5x) ?

The limit as x approaches 0 of 8xcsc(5x) is 8/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of 8xcsc(5x)

x \to 0 lim (8 x csc (5 x))

\frac{8}{5}

Decimal

1.6

Solution steps

x \to 0 lim (8 x csc (5 x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 8 \cdot x \to 0 lim (x csc (5 x))

Express with sin, cos

= 8 \cdot x \to 0 lim (\frac{x}{sin ( 5 x )})

Apply L'Hopital's Rule

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

= 8 \cdot x \to 0 lim (\frac{1}{cos ( 5 x ) \cdot 5})

Plug in the value

x = 0

= 8 \cdot \frac{1}{cos ( 5 \cdot 0 ) \cdot 5}

Simplify

8 \cdot \frac{1}{cos ( 5 \cdot 0 ) \cdot 5} : \frac{8}{5}

= \frac{8}{5}

11 (t + 1) \frac{d y}{d t} - 8 y = 24 t

y^{^{'}} + e^{x} y = e^{x}

\frac{d}{d t} (t - \frac{1}{t})

\frac{d y}{d x} = e^{\frac{y}{x}} + \frac{y}{x}

\int x^{3} (9 + x^{4})^{6} d x

What is the limit as x approaches 0 of 8xcsc(5x) ?
The limit as x approaches 0 of 8xcsc(5x) is 8/5