What is the limit as x approaches 0 of f(x)(x^3-x) ?

The limit as x approaches 0 of f(x)(x^3-x) is 0

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limit as x approaches 0 of f(x)(x^3-x)

x \to 0 lim (f (x) (x^{3} - x))

0

Solution steps

x \to 0 lim (f (x) (x^{3} - x))

Plug in the value

x = 0

, assuming the function is continuous at this point

= f (0) (0^{3} - 0)

Simplify

= 0

x \to 4 lim (\frac{x ^{3} - 16 x}{x ^{2} - 4 x})

x \to 0 lim (\frac{x}{x ^{2} - 8 x})

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

x \to 5 lim (8 - x - x^{2})

x \to 2 lim (\frac{sin ( 8 x )}{x})

What is the limit as x approaches 0 of f(x)(x^3-x) ?
The limit as x approaches 0 of f(x)(x^3-x) is 0