What is the limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)} ?

The limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)} is 0

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 (9sin(x))/(\sqrt[3]{x)}

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( x )}{\frac{1}{3 x ^{\frac{2}{3}}}})

= 9 \cdot x \to 0 lim (\frac{cos ( x )}{\frac{1}{3 x ^{\frac{2}{3}}}})

Simplify

= 9 \cdot x \to 0 lim (3 x^{\frac{2}{3}} cos (x))

Plug in the value

x = 0

= 9 \cdot 3 \cdot 0^{\frac{2}{3}} cos (0)

Simplify

9 \cdot 3 \cdot 0^{\frac{2}{3}} cos (0) : 0

= 0

\frac{d}{d x} (4 x cos (x))

\frac{d}{d x} (\frac{2}{3} x^{- \frac{1}{3}})

\int (\frac{x}{y}) d y

\int_{4}^{\infty} e^{4 x} d x

\int 5 - x^{2} d x

What is the limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)} ?
The limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)} is 0