What is the limit as x approaches 0-of (x+5)/x ?

The limit as x approaches 0-of (x+5)/x is -infinity

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limit as x approaches 0-of (x+5)/x

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

- \infty

Solution steps

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

Divide by highest denominator power:

1 + \frac{5}{x}

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

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

With the exception of indeterminate form

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

x \to 0 - lim (1) = 1

x \to 0 - lim (\frac{5}{x}) = - \infty

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

x \to 4 lim (3 3 - x)

x \to 0 lim (\frac{1}{x + 4} - \frac{1}{4})

x \to 7 lim (g (x))

x \to 2 lim (\frac{x ^{2} - 9}{x + 3})

x \to 0 lim (\frac{2 x + sin ( x )}{x})

What is the limit as x approaches 0-of (x+5)/x ?
The limit as x approaches 0-of (x+5)/x is -infinity