What is the limit as x approaches 1 of x/(|3x-4|) ?

The limit as x approaches 1 of x/(|3x-4|) is 1

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limit as x approaches 1 of x/(|3x-4|)

x \to 1 lim (\frac{x}{∣ 3 x - 4 ∣})

1

Solution steps

x \to 1 lim (\frac{x}{∣ 3 x - 4 ∣})

Plug in the value

x = 1

= \frac{1}{∣ 3 \cdot 1 - 4 ∣}

Simplify

\frac{1}{∣ 3 \cdot 1 - 4 ∣} : 1

= 1

x \to \infty lim (x \cdot \frac{π}{2})

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

x \to \infty lim (\frac{5 x ^{2}}{e ^{x^{3}}})

x \to 0 - lim (\frac{x}{1 - cos ( x )})

x \to 0 lim (\frac{2 e ^{3 x} - 2}{ln ( x + 1 ) - 3 x ^{3}})

What is the limit as x approaches 1 of x/(|3x-4|) ?
The limit as x approaches 1 of x/(|3x-4|) is 1