What is the limit as x approaches 1+of (4x)/(2x-2) ?

The limit as x approaches 1+of (4x)/(2x-2) is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 1+of (4x)/(2x-2)

x \to 1 + lim (\frac{4 x}{2 x - 2})

\infty

Solution steps

x \to 1 + lim (\frac{4 x}{2 x - 2})

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

= 4 \cdot x \to 1 + lim (\frac{x}{2 x - 2})

Factor out

2 x

from

2 x - 2 : 2 x (1 - \frac{2}{2 x})

= 4 \cdot x \to 1 + lim (\frac{x}{2 x ( 1 - \frac{2}{2 x} )})

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

= 4 \cdot \frac{1}{2} \cdot x \to 1 + lim (\frac{x}{x ( 1 - \frac{2}{2 x} )})

Simplify

\frac{x}{x ( 1 - \frac{2}{2 x} )} : \frac{x}{x - 1}

= 4 \cdot \frac{1}{2} \cdot x \to 1 + lim (\frac{x}{x - 1})

Divide by highest denominator power:

\frac{1}{1 - \frac{1}{x}}

= 4 \cdot \frac{1}{2} \cdot x \to 1 + lim (\frac{1}{1 - \frac{1}{x}})

For

x

approaching

1

from the right

, x > 1 \Rightarrow 1 - \frac{1}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 4 \cdot \frac{1}{2} \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 lim (g (x) sin (\frac{1}{x}))

\frac{d}{d x} (sec (x) tan (x))

\frac{\partial}{\partial x} (2 y ln (x))

\frac{d}{d x} (1 0^{s i n (π x)})

\int \frac{x}{16 - 9 x ^{2}} d x

What is the limit as x approaches 1+of (4x)/(2x-2) ?
The limit as x approaches 1+of (4x)/(2x-2) is infinity