What is the limit as x approaches 0 of x+e^{-x} ?

The limit as x approaches 0 of x+e^{-x} is 1

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limit as x approaches 0 of x+e^{-x}

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

1

Solution steps

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

Plug in the value

x = 0

= 0 + e^{- 0}

Simplify

= 1

x \to \frac{π}{2} - lim (\frac{tan ( x )}{\frac{3}{2 x - π}})

x \to 1 lim (\frac{1}{1 - x})

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

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

x \to - \infty lim (16 x^{3})

What is the limit as x approaches 0 of x+e^{-x} ?
The limit as x approaches 0 of x+e^{-x} is 1