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

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

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

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