What is the limit as x approaches 0-of (sqrt(x+1))/x ?

The limit as x approaches 0-of (sqrt(x+1))/x is -infinity

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limit as x approaches 0-of (sqrt(x+1))/x

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

- \infty

Solution steps

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

\frac{x + 1}{x} = \frac{1}{x} x + 1

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

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

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

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

x \to 0 - lim (x + 1) = 1

= (- \infty) \cdot 1

Apply Infinity Property:

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

= - \infty

x \to a + lim (f (x))

x \to 0 + lim ((x^{x})^{x})

x \to 5 - lim ((x - 5) \cdot ln (5 - x))

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

x \to 2 lim (\frac{∣ x + 2 ∣}{x + 2})

What is the limit as x approaches 0-of (sqrt(x+1))/x ?
The limit as x approaches 0-of (sqrt(x+1))/x is -infinity