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

Apply Infinity Property:

c - \infty = - \infty

= - \infty

x \to \infty lim (x^{11})

x \to 0 lim (\frac{x}{n 1 + a x k 1 + b x - 1})

x \to \infty lim (4 x^{2} - 7 x - 2 x)

x \to 0 lim (\frac{( 9 ^{x} - 8 ^{x} )}{x})

x \to \infty lim (50)

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