What is the limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x ?

The limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x is infinity

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limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x

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

\infty

Solution steps

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

x \to 3 + lim (\frac{3}{x - 3}) = \infty

x \to 3 + lim (2 x) = 6

= \infty - 6

Apply Infinity Property:

\infty - c = \infty

= \infty

What is the limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x ?
The limit as x approaches 3+of (sqrt(3))/(sqrt(x)-\sqrt{3)}-2x is infinity