What is the limit as x approaches infinity of 20+5e^{-5x} ?

The limit as x approaches infinity of 20+5e^{-5x} is 20

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limit as x approaches infinity of 20+5e^{-5x}

x \to \infty lim (20 + 5 e^{- 5 x})

20

Solution steps

x \to \infty lim (20 + 5 e^{- 5 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 \infty lim (20) + x \to \infty lim (5 e^{- 5 x})

x \to \infty lim (20) = 20

x \to \infty lim (5 e^{- 5 x}) = 0

= 20 + 0

Simplify

= 20

x \to 0 lim (x ln (x^{5}))

x \to - 4 lim (\frac{1}{x - 4})

x \to 1 - lim (e^{(\frac{1}{x ^{2} - 1})})

x \to - 2 lim (x^{2} - 2 x - 1)

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

What is the limit as x approaches infinity of 20+5e^{-5x} ?
The limit as x approaches infinity of 20+5e^{-5x} is 20