What is the limit as x approaches 5 of (x^2-2)/(x-5) ?

The limit as x approaches 5 of (x^2-2)/(x-5) is diverges

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limit as x approaches 5 of (x^2-2)/(x-5)

x \to 5 lim (\frac{x ^{2} - 2}{x - 5})

diverges

Solution steps

x \to 5 lim (\frac{x ^{2} - 2}{x - 5})

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

then the limit does not exist

x \to 5 + lim (\frac{x ^{2} - 2}{x - 5}) = \infty

x \to 5 - lim (\frac{x ^{2} - 2}{x - 5}) = - \infty

= diverges

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

x \to - 3 lim (\frac{1}{( x + 3 ) ^{4}})

x \to 0 lim (+ \frac{ln ( x )}{x})

x \to 0 lim (\frac{1 - x ^{2}}{x})

x \to 0 lim (e^{\frac{1}{x}} \cdot x)

What is the limit as x approaches 5 of (x^2-2)/(x-5) ?
The limit as x approaches 5 of (x^2-2)/(x-5) is diverges