What is the limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4) ?

The limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4) is 16/7

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limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4)

x \to 4 lim (\frac{3 x ^{2} - 8 x - 16}{2 x ^{2} - 9 x + 4})

\frac{16}{7}

Decimal

2.28571 \dots

Solution steps

x \to 4 lim (\frac{3 x ^{2} - 8 x - 16}{2 x ^{2} - 9 x + 4})

Simplify

\frac{3 x ^{2} - 8 x - 16}{2 x ^{2} - 9 x + 4} : \frac{3 x + 4}{2 x - 1}

= x \to 4 lim (\frac{3 x + 4}{2 x - 1})

Plug in the value

x = 4

= \frac{3 \cdot 4 + 4}{2 \cdot 4 - 1}

Simplify

= \frac{16}{7}

What is the limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4) ?
The limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4) is 16/7