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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\infty

Solution steps

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

\frac{2 x + 1}{x - 2} = (2 x + 1) \frac{1}{x - 2}

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

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

With the exception of indeterminate form

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

x \to 2 + lim (2 x + 1) = 5

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

= 5 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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