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

The limit as x approaches 8 of (x^2-sqrt(8x))/(x^3+2x^2) is 7/80

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

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

\frac{7}{80}

Decimal

0.0875

Solution steps

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

Plug in the value

x = 8

= \frac{8 ^{2} - 8 \cdot 8}{8 ^{3} + 2 \cdot 8 ^{2}}

Simplify

\frac{8 ^{2} - 8 \cdot 8}{8 ^{3} + 2 \cdot 8 ^{2}} : \frac{7}{80}

= \frac{7}{80}

What is the limit as x approaches 8 of (x^2-sqrt(8x))/(x^3+2x^2) ?
The limit as x approaches 8 of (x^2-sqrt(8x))/(x^3+2x^2) is 7/80