What is the limit as x approaches 5-of (5x)/(x^2-25) ?

The limit as x approaches 5-of (5x)/(x^2-25) is -infinity

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limit as x approaches 5-of (5x)/(x^2-25)

x \to 5 - lim (\frac{5 x}{x ^{2} - 25})

- \infty

Solution steps

x \to 5 - lim (\frac{5 x}{x ^{2} - 25})

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

= 5 \cdot x \to 5 - lim (\frac{x}{x ^{2} - 25})

\frac{x}{x ^{2} - 25} = x \frac{1}{x ^{2} - 25}

= 5 \cdot x \to 5 - lim (x \frac{1}{x ^{2} - 25})

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

With the exception of indeterminate form

= 5 \cdot x \to 5 - lim (x) \cdot x \to 5 - lim (\frac{1}{x ^{2} - 25})

x \to 5 - lim (x) = 5

x \to 5 - lim (\frac{1}{x ^{2} - 25}) = - \infty

= 5 \cdot 5 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 0 + lim ([- ln (x)]^{x})

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

x \to 0 lim (x^{4} - 4 ln (x))

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

x \to \infty lim (+ x \cdot 0)

What is the limit as x approaches 5-of (5x)/(x^2-25) ?
The limit as x approaches 5-of (5x)/(x^2-25) is -infinity