What is the limit as x approaches 0-of xe^{2/x} ?

The limit as x approaches 0-of xe^{2/x} is 0

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limit as x approaches 0-of xe^{2/x}

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

0

Solution steps

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

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

With the exception of indeterminate form

= x \to 0 - lim (x) \cdot x \to 0 - lim (e^{\frac{2}{x}})

x \to 0 - lim (x) = 0

x \to 0 - lim (e^{\frac{2}{x}}) = 0

= 0 \cdot 0

Simplify

= 0

\int_{0}^{2} x e^{- x^{2}} d x

\int_{0}^{\frac{3 π}{2}} ∣ cos (x) ∣ d x

f (x) = \frac{2}{2 x + 1}

\frac{2 z ^{3}}{3} - z

f (t) = e^{2 t s i n (2 t)}

What is the limit as x approaches 0-of xe^{2/x} ?
The limit as x approaches 0-of xe^{2/x} is 0