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

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

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

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

27

Solution steps

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

Simplify

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

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

Plug in the value

x = \frac{3}{2}

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

Simplify

4 (\frac{3}{2})^{2} + 6 \cdot \frac{3}{2} + 9 : 27

= 27

\frac{d}{d x} (x^{2} e^{x} + 2 x e^{x})

x \to \infty lim (\frac{ln ( 5 )}{( 1 + ln ( x ) )})

x \to 0 + lim (x e^{s i n (\frac{π}{x})})

\frac{d}{d x} ((\frac{10 + x}{π})^{\frac{1}{3}})

\int - \frac{1}{1 - x} d x

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