What is the limit as x approaches infinity of (x^2+1)/(x+2) ?

The limit as x approaches infinity of (x^2+1)/(x+2) is infinity

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limit as x approaches infinity of (x^2+1)/(x+2)

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

\infty

Solution steps

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

Divide by highest denominator power:

\frac{x + \frac{1}{x}}{1 + \frac{2}{x}}

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( x + \frac{1}{x} )}{lim _{x \to \infty} ( 1 + \frac{2}{x} )}

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

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

= \frac{\infty}{1}

Apply Infinity Property:

\frac{\infty}{c} = \infty

= \infty

What is the limit as x approaches infinity of (x^2+1)/(x+2) ?
The limit as x approaches infinity of (x^2+1)/(x+2) is infinity