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

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

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

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

\infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

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

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

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

x \to \infty lim (1) = 1

= \frac{1}{2} (\infty + 1)

Simplify

\frac{1}{2} (\infty + 1) : \infty

= \infty

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