What is the limit as x approaches infinity of |x+2| ?

The limit as x approaches infinity of |x+2| is infinity

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limit as x approaches infinity of |x+2|

x \to \infty lim (∣ x + 2 ∣)

\infty

Solution steps

x \to \infty lim (∣ x + 2 ∣)

x + 2

is positive when

x \to \infty

. Therefore

∣ x + 2 ∣ = x + 2

= x \to \infty lim (x + 2)

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

\int_{0}^{\infty} \frac{1}{2 x + 5} d x

\int_{0}^{1} \frac{1}{2 t ^{2} - 2 t + 1} d t

\frac{1}{1 - x ^{2}}, 0

\frac{d}{d x} (- \frac{x}{5})

x \to 2 lim (3 x^{3} - 5 x)

What is the limit as x approaches infinity of |x+2| ?
The limit as x approaches infinity of |x+2| is infinity