What is the limit as x approaches 4 of x/(4-x)-x^3 ?

The limit as x approaches 4 of x/(4-x)-x^3 is diverges

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limit as x approaches 4 of x/(4-x)-x^3

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

diverges

Solution steps

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

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} - x^{3}) = - \infty

x \to 4 - lim (\frac{x}{4 - x} - x^{3}) = \infty

= diverges

What is the limit as x approaches 4 of x/(4-x)-x^3 ?
The limit as x approaches 4 of x/(4-x)-x^3 is diverges