What is the limit as x approaches 1 of (2x+|x|)/(3x) ?

The limit as x approaches 1 of (2x+|x|)/(3x) is 1

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limit as x approaches 1 of (2x+|x|)/(3x)

x \to 1 lim (\frac{2 x + ∣ x ∣}{3 x})

1

Solution steps

x \to 1 lim (\frac{2 x + ∣ x ∣}{3 x})

Plug in the value

x = 1

= \frac{2 \cdot 1 + ∣ 1 ∣}{3 \cdot 1}

Simplify

\frac{2 \cdot 1 + ∣ 1 ∣}{3 \cdot 1} : 1

= 1

x \to 2 - lim (\frac{x}{x ^{3} - 8})

x \to 0 + lim (\frac{1}{x} ln (x))

x \to \infty lim (x - x^{3})

x \to π + lim (\frac{x}{csc ( x )})

x \to a lim (\frac{a - x}{x - a})

What is the limit as x approaches 1 of (2x+|x|)/(3x) ?
The limit as x approaches 1 of (2x+|x|)/(3x) is 1