What is the limit as x approaches infinity of 4x+1/x ?

The limit as x approaches infinity of 4x+1/x is infinity

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limit as x approaches infinity of 4x+1/x

x \to \infty lim (4 x + \frac{1}{x})

\infty

Solution steps

x \to \infty lim (4 x + \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 (4 x) + x \to \infty lim (\frac{1}{x})

x \to \infty lim (4 x) = \infty

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

= \infty + 0

Apply Infinity Property:

\infty + c = \infty

= \infty

What is the limit as x approaches infinity of 4x+1/x ?
The limit as x approaches infinity of 4x+1/x is infinity