What is the limit as x approaches 5-of (3x)/(x^2-5x) ?

The limit as x approaches 5-of (3x)/(x^2-5x) is -infinity

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limit as x approaches 5-of (3x)/(x^2-5x)

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

- \infty

Solution steps

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

Simplify

\frac{3 x}{x ^{2} - 5 x} : \frac{3}{x - 5}

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

For

x

approaching

5

from the left

, x < 5 \Rightarrow x - 5 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

x \to 1 lim (x^{4} - x^{2} + x - 2)

x \to 1 lim (\frac{I n x}{x ^{2} - 1})

x \to 5 lim (x^{2} - 3 x + 4)

x \to - \infty lim (\frac{3 e ^{x} - 4 e ^{- x}}{2 e ^{x} + e ^{- x}})

x \to 8 lim (7 x + 9)

What is the limit as x approaches 5-of (3x)/(x^2-5x) ?
The limit as x approaches 5-of (3x)/(x^2-5x) is -infinity