What is the limit as x approaches infinity of sqrt(x+1) ?

The limit as x approaches infinity of sqrt(x+1) is infinity

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limit as x approaches infinity of sqrt(x+1)

x \to \infty lim (x + 1)

\infty

Solution steps

x \to \infty lim (x + 1)

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= x \to \infty lim (x + 1)

Apply Infinity Property:

x \to \infty lim (a x^{n} + \dots + b x + c) = \infty, a > 0,

n is odd

a = 1, n = 1

= \infty

Apply Infinity Property:

\infty^{c} = \infty

= \infty

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What is the limit as x approaches infinity of sqrt(x+1) ?
The limit as x approaches infinity of sqrt(x+1) is infinity