What is the limit as x approaches 2/3 of (27x^3-8)/(9x^2-4) ?

The limit as x approaches 2/3 of (27x^3-8)/(9x^2-4) is 3

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limit as x approaches 2/3 of (27x^3-8)/(9x^2-4)

x \to \frac{2}{3} lim (\frac{27 x ^{3} - 8}{9 x ^{2} - 4})

3

Solution steps

x \to \frac{2}{3} lim (\frac{27 x ^{3} - 8}{9 x ^{2} - 4})

Simplify

\frac{27 x ^{3} - 8}{9 x ^{2} - 4} : \frac{9 x ^{2} + 6 x + 4}{3 x + 2}

= x \to \frac{2}{3} lim (\frac{9 x ^{2} + 6 x + 4}{3 x + 2})

Plug in the value

x = \frac{2}{3}

= \frac{9 ( \frac{2}{3} ) ^{2} + 6 \cdot \frac{2}{3} + 4}{3 \cdot \frac{2}{3} + 2}

Simplify

\frac{9 ( \frac{2}{3} ) ^{2} + 6 \cdot \frac{2}{3} + 4}{3 \cdot \frac{2}{3} + 2} : 3

= 3

t y^{^{'''}} - y^{^{''}} = 0

8 - x

f (x) = \frac{cos ( x )}{x ^{3}}

x \to 5 lim (2 x^{2} - 7 x + 13)

\frac{\partial}{\partial x} ((2 x + y - 4) e^{2 y})

What is the limit as x approaches 2/3 of (27x^3-8)/(9x^2-4) ?
The limit as x approaches 2/3 of (27x^3-8)/(9x^2-4) is 3