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

The limit as x approaches 2 of (2x)/(4-x^2) is diverges

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limit as x approaches 2 of (2x)/(4-x^2)

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

diverges

Solution steps

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

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

then the limit does not exist

x \to 2 + lim (\frac{2 x}{4 - x ^{2}}) = - \infty

x \to 2 - lim (\frac{2 x}{4 - x ^{2}}) = \infty

= diverges

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

x \to \infty lim (\frac{4 x ^{3} + 2 x - 24}{x ^{4} - x ^{2} + 84})

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

x \to 3 lim (\frac{5 - 2 x}{x - 3})

x \to 7 - lim (\frac{x - x}{x - 7})

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