espandere x/(Δy(y+Δy)^2)

Soluzione

espandere

\frac{x}{Δ y ( y + Δ y ) ^{2}}

\frac{x}{Δ y ^{3} + 2 Δ ^{2} y ^{3} + Δ ^{3} y ^{3}}

Fasi della soluzione

\frac{x}{Δ y ( y + Δ y ) ^{2}}

(y + Δ y)^{2} = y^{2} + 2Δ y^{2} + Δ^{2} y^{2}

= \frac{x}{Δ y ( y ^{2} + 2Δ y ^{2} + Δ ^{2} y ^{2} )}

Espandi

Δ y (y^{2} + 2Δ y^{2} + Δ^{2} y^{2}) : Δ y^{3} + 2 Δ^{2} y^{3} + Δ^{3} y^{3}

= \frac{x}{Δ y ^{3} + 2 Δ ^{2} y ^{3} + Δ ^{3} y ^{3}}

e x p an d \frac{x ^{4} - ( m + 2 ) x ^{3} + m x ^{2} + x + m ^{2} + m}{x - m - 1}

e x p an d 10 (e^{\frac{x}{20}} + e^{- \frac{x}{20}})

e x p an d 3 9 - (3)^{2}

e x p an d \frac{x + 1}{( x ^{2} + 1 ) ( x ^{2} + 9 )}

e x p an d \frac{40000}{x ( 1000 - x )}