What is the limit as x approaches 0 of 1/(x(1+x^2)) ?

The limit as x approaches 0 of 1/(x(1+x^2)) is diverges

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limit as x approaches 0 of 1/(x(1+x^2))

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

diverges

Solution steps

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

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

then the limit does not exist

x \to 0 + lim (\frac{1}{x ( 1 + x ^{2} )}) = \infty

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

= diverges

x \to 3 lim (0. 5^{x})

x \to 8 lim (3 8 x)

x \to - 3 + lim (\frac{- 2 x ^{2}}{( x - 1 ) ( x + 3 )})

x \to 0 lim (2 x^{2} \cdot cot^{2} (x))

x \to \frac{π}{2} lim (sin (x) + 1)

What is the limit as x approaches 0 of 1/(x(1+x^2)) ?
The limit as x approaches 0 of 1/(x(1+x^2)) is diverges