If-y-1-x-2-x-3-and-x-1-where-is-small-show-that-y-3-5-Hence-find-the-increase-in-y-when-x-is-increased-from-1-to-1-02-

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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