What is the limit as x approaches 0 of x(e^x+1/x) ?

The limit as x approaches 0 of x(e^x+1/x) is 1

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limit as x approaches 0 of x(e^x+1/x)

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

1

Solution steps

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

Simplify

x (e^{x} + \frac{1}{x}) : e^{x} x + 1

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

Plug in the value

x = 0

= e^{0} \cdot 0 + 1

Simplify

= 1

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What is the limit as x approaches 0 of x(e^x+1/x) ?
The limit as x approaches 0 of x(e^x+1/x) is 1