What is the limit as x approaches 4 of (x-4)/(2-sqrt(8-x)) ?

The limit as x approaches 4 of (x-4)/(2-sqrt(8-x)) is 4

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limit as x approaches 4 of (x-4)/(2-sqrt(8-x))

x \to 4 lim (\frac{x - 4}{2 - 8 - x})

4

Solution steps

x \to 4 lim (\frac{x - 4}{2 - 8 - x})

Rationalize denominator

\frac{x - 4}{2 - 8 - x} : 2 + - x + 8

= x \to 4 lim (2 + - x + 8)

Plug in the value

x = 4

= 2 + - 4 + 8

Simplify

2 + - 4 + 8 : 4

= 4

What is the limit as x approaches 4 of (x-4)/(2-sqrt(8-x)) ?
The limit as x approaches 4 of (x-4)/(2-sqrt(8-x)) is 4