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

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

limit as x approaches infinity of 3/(e^{-x)+2}

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

\frac{3}{2}

Decimal

1.5

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to \infty lim (\frac{1}{e ^{- x} + 2})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 3 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{- x} + 2 )}

x \to \infty lim (1) = 1

x \to \infty lim (e^{- x} + 2) = 2

= 3 \cdot \frac{1}{2}

Simplify

3 \cdot \frac{1}{2} : \frac{3}{2}

= \frac{3}{2}

x \to 0 lim (\frac{x + 1}{x ^{2}})

x \to 0 lim (2 x ln (x))

n \to \infty lim (0^{n})

x \to 0 lim (e^{x^{3}} - 1)

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

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