What is the limit as y approaches 0 of (4y^5+5y^3)/(y^4-y) ?

The limit as y approaches 0 of (4y^5+5y^3)/(y^4-y) is 0

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limit as y approaches 0 of (4y^5+5y^3)/(y^4-y)

y \to 0 lim (\frac{4 y ^{5} + 5 y ^{3}}{y ^{4} - y})

0

Solution steps

y \to 0 lim (\frac{4 y ^{5} + 5 y ^{3}}{y ^{4} - y})

Simplify

\frac{4 y ^{5} + 5 y ^{3}}{y ^{4} - y} : \frac{y ^{2} ( 4 y ^{2} + 5 )}{y ^{3} - 1}

= y \to 0 lim (\frac{y ^{2} ( 4 y ^{2} + 5 )}{y ^{3} - 1})

Plug in the value

y = 0

= \frac{0 ^{2} ( 4 \cdot 0 ^{2} + 5 )}{0 ^{3} - 1}

Simplify

\frac{0 ^{2} ( 4 \cdot 0 ^{2} + 5 )}{0 ^{3} - 1} : 0

= 0

\int - \frac{x}{1 + x} d x

6 - y = x^{2}, y + 8 = x^{2}, x - y + 4 = 0, x - y - 6 = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

\frac{d}{d x} (\frac{1}{x + sin ( x )})

\frac{d y}{d x} = \frac{4 e ^{4 x}}{e ^{y}}

What is the limit as y approaches 0 of (4y^5+5y^3)/(y^4-y) ?
The limit as y approaches 0 of (4y^5+5y^3)/(y^4-y) is 0