What is the limit as x approaches 0+of x^2*sin(1/x) ?

The limit as x approaches 0+of x^2*sin(1/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 x^2*sin(1/x)

x \to 0 + lim (x^{2} \cdot sin (\frac{1}{x}))

0

Solution steps

x \to 0 + lim (x^{2} sin (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= 0

x \to 0 + lim (\frac{∣ sin ( x ) ∣}{x})

x \to 0 lim (+ (sin (\frac{1}{x})))

θ \to 0 lim (cot (θ) - csc (θ))

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

x \to 0 + lim (\frac{4}{x})

What is the limit as x approaches 0+of x^2*sin(1/x) ?
The limit as x approaches 0+of x^2*sin(1/x) is 0