What is the limit as x approaches 0+of 1+xe^{(2/x)} ?

The limit as x approaches 0+of 1+xe^{(2/x)} is infinity

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limit as x approaches 0+of 1+xe^{(2/x)}

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

\infty

Solution steps

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

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

With the exception of indeterminate form

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

x \to 0 + lim (1) = 1

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

= 1 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

\frac{d y}{d x} = 2 y + y^{5}, y (0) = 1

\int e^{6 t} d t

f (x) = \frac{A}{x ^{10}} + B e^{x}

y^{^{'}} - 5 y = 6 e^{5 x}, y (0) = 0

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

What is the limit as x approaches 0+of 1+xe^{(2/x)} ?
The limit as x approaches 0+of 1+xe^{(2/x)} is infinity