What is the limit as x approaches 0 of (x^3+8x)/(3x) ?

The limit as x approaches 0 of (x^3+8x)/(3x) is 8/3

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limit as x approaches 0 of (x^3+8x)/(3x)

x \to 0 lim (\frac{x ^{3} + 8 x}{3 x})

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

x \to 0 lim (\frac{x ^{3} + 8 x}{3 x})

Simplify

\frac{x ^{3} + 8 x}{3 x} : \frac{1}{3} (x^{2} + 8)

= x \to 0 lim (\frac{1}{3} (x^{2} + 8))

Plug in the value

x = 0

= \frac{1}{3} (0^{2} + 8)

Simplify

\frac{1}{3} (0^{2} + 8) : \frac{8}{3}

= \frac{8}{3}

x \to 5 - lim (\frac{1}{( 5 - x ) ^{2}})

x \to 5 lim (\frac{x ^{3} - 8}{x - 2})

x \to 0 lim (\frac{5}{ln ( x ^{2} )})

x \to 0 lim (\frac{( 1 + x ^{4} ) - 1}{x})

x \to \infty lim (\frac{tanh ( x )}{x})

What is the limit as x approaches 0 of (x^3+8x)/(3x) ?
The limit as x approaches 0 of (x^3+8x)/(3x) is 8/3