What is the limit as x approaches infinity of 5-1/x ?

The limit as x approaches infinity of 5-1/x is 5

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limit as x approaches infinity of 5-1/x

x \to \infty lim (5 - \frac{1}{x})

5

Solution steps

x \to \infty lim (5 - \frac{1}{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 (5) - x \to \infty lim (\frac{1}{x})

x \to \infty lim (5) = 5

x \to \infty lim (\frac{1}{x}) = 0

= 5 - 0

Simplify

= 5

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

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

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

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

x \to 0 lim (cos (x) \frac{1}{x})

What is the limit as x approaches infinity of 5-1/x ?
The limit as x approaches infinity of 5-1/x is 5