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

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

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limit as x approaches infinity of 1/x-x

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

- \infty

Solution steps

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

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

x \to \infty lim (x) = \infty

= 0 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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

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

x \to 2 lim (\frac{\frac{8}{x} - 4}{x - 2})

x \to 1 lim (x^{2} - 3 x)

x \to 0 lim (x^{π x})

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