What is the limit as x approaches 3 of x*e^{1/(x^2)} ?

The limit as x approaches 3 of x*e^{1/(x^2)} is 3e^{1/9}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 3 of x*e^{1/(x^2)}

x \to 3 lim (x \cdot e^{\frac{1}{x ^{2}}})

3 e^{\frac{1}{9}}

Decimal Notation

3.35255 \dots

Solution steps

x \to 3 lim (x e^{\frac{1}{x ^{2}}})

Plug in the value

x = 3

= 3 e^{\frac{1}{3 ^{2}}}

Simplify

= 3 e^{\frac{1}{9}}

x \to 3 lim (x \cdot e^{\frac{1}{x}})

x \to 3 lim (\frac{( 1 + x ) ^{2} - 1}{x})

x \to 3 lim (\frac{3}{x ^{5}})

x \to 3 lim (\frac{1}{sin ( x )})

x \to 3 lim (3 x^{2} - 5 x + 8)

What is the limit as x approaches 3 of x*e^{1/(x^2)} ?
The limit as x approaches 3 of x*e^{1/(x^2)} is 3e^{1/9}