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

f (x) = x^{2} + 3 x - 3, at x = 1

f (t) = e^{5 t s i n (2 t)}

15 (cos (x) - x sin (x))

x \to 1 - lim (\frac{6}{x ^{3} - 1})

x \to 0 + lim (tan^{x} (2 x))

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