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

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

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limit as x approaches 0-of (2x-1)/(xe^x)

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

\infty

Solution steps

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

Expand

\frac{2 x - 1}{x e ^{x}} : \frac{2}{e ^{x}} - \frac{1}{e ^{x} x}

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

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

x \to 0 - lim (\frac{1}{e ^{x} x}) = - \infty

= 2 - (- \infty)

Simplify

2 - (- \infty) : \infty

= \infty

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