What is the limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2) ?

The limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2) is h/5

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limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2)

x \to 0 lim (\frac{x ^{2} h + 3 x h ^{2} + h ^{3}}{2 x h + 5 h ^{2}})

\frac{h}{5}

Solution steps

x \to 0 lim (\frac{x ^{2} h + 3 x h ^{2} + h ^{3}}{2 x h + 5 h ^{2}})

Plug in the value

x = 0

= \frac{0 ^{2} h + 3 \cdot 0 \cdot h ^{2} + h ^{3}}{2 \cdot 0 \cdot h + 5 h ^{2}}

Simplify

\frac{0 ^{2} h + 3 \cdot 0 \cdot h ^{2} + h ^{3}}{2 \cdot 0 \cdot h + 5 h ^{2}} : \frac{h}{5}

= \frac{h}{5}

What is the limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2) ?
The limit as x approaches 0 of (x^2h+3xh^2+h^3)/(2xh+5h^2) is h/5