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

y \to - 2 lim (g (y))

x \to 0 lim (e^{x} cos (4 x))

x \to 5 - lim (x - 5)

x \to 0 lim (\frac{6}{x} + \frac{6}{x ^{2} - x})

x \to - 0 lim (x ln (x))

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