What is the limit as x approaches 1+of (3x)/(x-1) ?

The limit as x approaches 1+of (3x)/(x-1) is infinity

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limit as x approaches 1+of (3x)/(x-1)

x \to 1 + lim (\frac{3 x}{x - 1})

\infty

Solution steps

x \to 1 + lim (\frac{3 x}{x - 1})

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

= 3 \cdot x \to 1 + lim (\frac{x}{x - 1})

Divide by highest denominator power:

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

= 3 \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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to - 2 lim (\frac{∣ x ∣}{x})

x \to a lim (x + 4)

x \to 3 lim ((x + 3) (x - 5))

x \to 0 lim (\frac{2 sec ( x )}{csc ( x )})

z \to 0 lim (\frac{1}{sin ( z )})

What is the limit as x approaches 1+of (3x)/(x-1) ?
The limit as x approaches 1+of (3x)/(x-1) is infinity