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

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

d er i v a t i v e f (x) = \frac{cos ( x )}{x ^{3}}

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

\int \frac{e ^{8 s i n (x)}}{sec ( x )} d x

\int (2 - e^{- x})^{2} d x

(x csc (\frac{y}{x}) - y) d x + x d y = 0

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