What is the limit as x approaches+0 of (3x)/(xe^x) ?

The limit as x approaches+0 of (3x)/(xe^x) is 3

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limit as x approaches+0 of (3x)/(xe^x)

x \to + 0 lim (\frac{3 x}{x e ^{x}})

3

Solution steps

x \to 0 lim (\frac{3 x}{x e ^{x}})

Cancel the common factor:

x

= x \to 0 lim (\frac{3}{e ^{x}})

Plug in the value

x = 0

= \frac{3}{e ^{0}}

Simplify

= 3

What is the limit as x approaches+0 of (3x)/(xe^x) ?
The limit as x approaches+0 of (3x)/(xe^x) is 3