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If y = f(x) = x2 + x, x = 10, ∆x = 0.1, find ∆y, dy. |
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Answer» Given y = x2 + x, x = 10 and ∆x = 0.1 ∆y = f(x + ∆x) – f(x) = (x + ∆x)2 + (x + ∆x) – (x2 + x) = x2 + 2x ∆x + (∆x)2 + x + ∆x – x2 – x = 2x ∆X + (∆x)2 + ∆x = 2(10) (0.1) + (0.1)2 + 0.1 = 2 + 0.01 + 0.1 = 2.11 dy = f1 (x) ∆x = (2x + 1) ∆x = {2.(10) + 1} (0.1) = (21) (0.1) = 2.10. |
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