What is the limit as x approaches 5 of (3x)/(|x-5|) ?

The limit as x approaches 5 of (3x)/(|x-5|) is infinity

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limit as x approaches 5 of (3x)/(|x-5|)

x \to 5 lim (\frac{3 x}{∣ x - 5 ∣})

\infty

Solution steps

x \to 5 lim (\frac{3 x}{∣ x - 5 ∣})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 5 - lim (\frac{3 x}{∣ x - 5 ∣}) = \infty

x \to 5 + lim (\frac{3 x}{∣ x - 5 ∣}) = \infty

= \infty

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

t \to 0 + lim (\frac{2}{t} - \frac{1}{e ^{t} - 1})

x \to 0 lim (\frac{( 1 - x ) ^{5} - 1}{x})

x \to 2 lim (4 x + 3)

x \to 2 lim (4 x + 2)

What is the limit as x approaches 5 of (3x)/(|x-5|) ?
The limit as x approaches 5 of (3x)/(|x-5|) is infinity