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

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

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

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

\infty

Solution steps

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

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

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

Divide by highest denominator power:

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

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

For

x

approaching

2

from the right

, x > 2 \Rightarrow 1 - \frac{2}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

Apply Infinity Property:

\infty^{c} = \infty

= \infty

x \to 4 lim (3 x - 1)

\frac{d}{d x} (\frac{5 x}{7 + x})

\frac{( x ^{3} - x )}{1 + x ^{2}}

\frac{( 1 + 16 t ^{2} )}{( 4 t ) ^{3}}

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3)

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