What is the limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) ?

The limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) is -5/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6)

x \to \frac{2}{3} lim (\frac{2 x ^{2} - 15 x + 18}{3 x ^{2} - 17 x - 6})

- \frac{5}{9}

Decimal

- 0.55555 \dots

Solution steps

x \to \frac{2}{3} lim (\frac{2 x ^{2} - 15 x + 18}{3 x ^{2} - 17 x - 6})

Plug in the value

x = \frac{2}{3}

= \frac{2 ( \frac{2}{3} ) ^{2} - 15 \cdot \frac{2}{3} + 18}{3 ( \frac{2}{3} ) ^{2} - 17 \cdot \frac{2}{3} - 6}

Simplify

\frac{2 ( \frac{2}{3} ) ^{2} - 15 \cdot \frac{2}{3} + 18}{3 ( \frac{2}{3} ) ^{2} - 17 \cdot \frac{2}{3} - 6} : - \frac{5}{9}

= - \frac{5}{9}

What is the limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) ?
The limit as x approaches 2/3 of (2x^2-15x+18)/(3x^2-17x-6) is -5/9