What is the limit as x approaches infinity of 1/x-3 ?

The limit as x approaches infinity of 1/x-3 is -3

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limit as x approaches infinity of 1/x-3

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

- 3

Solution steps

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

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

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

x \to \infty lim (3) = 3

= 0 - 3

Simplify

= - 3

What is the limit as x approaches infinity of 1/x-3 ?
The limit as x approaches infinity of 1/x-3 is -3