What is the limit as x approaches 4-of x/(sqrt(x)-2) ?

The limit as x approaches 4-of x/(sqrt(x)-2) is -infinity

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limit as x approaches 4-of x/(sqrt(x)-2)

x \to 4 - lim (\frac{x}{x - 2})

- \infty

Solution steps

x \to 4 - lim (\frac{x}{x - 2})

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

= x \to 4 - lim (x \frac{1}{x - 2})

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 4 - lim (x) \cdot x \to 4 - lim (\frac{1}{x - 2})

x \to 4 - lim (x) = 4

x \to 4 - lim (\frac{1}{x - 2}) = - \infty

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches 4-of x/(sqrt(x)-2) ?
The limit as x approaches 4-of x/(sqrt(x)-2) is -infinity