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}

y = x + 2, y = \frac{1}{x + 1}, x = 2, x = 0

\frac{\partial}{\partial x} (e^{y l n (x)})

\frac{d}{d x} (2 b x)

x \to \infty lim (\frac{1}{x ln ( x ) ( ln ( ln ( x ) ) ) ^{- 1}})

\int 5 e^{6 x} + \frac{- 3 x ^{6} + 4 x}{x ^{2}} d x

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