What is the limit as x approaches 0 of (x^3+6x)/x ?

The limit as x approaches 0 of (x^3+6x)/x is 6

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limit as x approaches 0 of (x^3+6x)/x

x \to 0 lim (\frac{x ^{3} + 6 x}{x})

6

Solution steps

x \to 0 lim (\frac{x ^{3} + 6 x}{x})

Simplify

\frac{x ^{3} + 6 x}{x} : x^{2} + 6

= x \to 0 lim (x^{2} + 6)

Plug in the value

x = 0

= 0^{2} + 6

Simplify

= 6

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What is the limit as x approaches 0 of (x^3+6x)/x ?
The limit as x approaches 0 of (x^3+6x)/x is 6