What is the limit as x approaches 0 of (x-1)/(x^3+x) ?

The limit as x approaches 0 of (x-1)/(x^3+x) is diverges

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limit as x approaches 0 of (x-1)/(x^3+x)

x \to 0 lim (\frac{x - 1}{x ^{3} + x})

diverges

Solution steps

x \to 0 lim (\frac{x - 1}{x ^{3} + x})

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

then the limit does not exist

x \to 0 + lim (\frac{x - 1}{x ^{3} + x}) = - \infty

x \to 0 - lim (\frac{x - 1}{x ^{3} + x}) = \infty

= diverges

What is the limit as x approaches 0 of (x-1)/(x^3+x) ?
The limit as x approaches 0 of (x-1)/(x^3+x) is diverges