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

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

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

x \to 1 + lim (\frac{3 x}{∣ 1 - x ∣})

\infty

Solution steps

x \to 1 + lim (\frac{3 x}{∣ 1 - x ∣})

1 - x

is negative when

x \to 1 +

. Therefore

∣ 1 - x ∣ = - 1 + x

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

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

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

Divide by highest denominator power:

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

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

For

x

approaching

1

from the right

, x > 1 \Rightarrow - \frac{1}{x} + 1 > 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 (sec (2 π))

x \to 1 lim (x sin (\frac{1}{x - 1}))

n \to \infty lim (i^{n})

x \to 0 lim (\frac{x ^{2}}{- 2})

x \to 2 lim (x^{4} - 2 x^{2})

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