If y=1+x^2 +x^3 and x=1+α, where α is small, show that y≈3+5α. Hence, find the increase in y when x is increased from 1 to 1.02


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Question Number 32110 by pieroo last updated on 19/Mar/18

$If y = 1 + x^{2} + x^{3} and x = 1 + α, where α is small, show$ $that y \approx 3 + 5 α . Hence, find the increase in y when$ $x is increased from 1 to 1.02$
	Answered by mrW2 last updated on 19/Mar/18

	$y = 1 + x^{2} + x^{3} = 1 + {(1 + α)}^{2} + {(1 + α)}^{3}$ $= 1 + 1 + 2 α + α^{2} + 1 + 3 α + 3 a^{2} + α^{3}$ $= 3 + 5 α + 4 α^{2} + α^{3}$ $\approx 3 + 5 α$ $y (1.02) \approx 3 + 5 \times 0.02 = 3.1$ $y (1) = 3$ $Δ y \approx 3.1 - 3 = 0.1$
	Commented by pieroo last updated on 19/Mar/18

	$thanks Sir$
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