What is the limit as x approaches 0+of 2+3e^{-3/x} ?

The limit as x approaches 0+of 2+3e^{-3/x} is 2

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limit as x approaches 0+of 2+3e^{-3/x}

x \to 0 + lim (2 + 3 e^{- \frac{3}{x}})

2

Solution steps

x \to 0 + lim (2 + 3 e^{- \frac{3}{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 (2) + x \to 0 + lim (3 e^{- \frac{3}{x}})

x \to 0 + lim (2) = 2

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

= 2 + 0

Simplify

= 2

\frac{1}{x - 1}

\frac{d}{d x} (x^{π^{2}} + (π^{2})^{x})

\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( 2 x )})

\frac{d}{d x} (e^{x - 1} - x + 1)

f (x) = x^{8} e^{x}

What is the limit as x approaches 0+of 2+3e^{-3/x} ?
The limit as x approaches 0+of 2+3e^{-3/x} is 2