The computation shows that the values of Δy and dy will be 0.572 and 0.4 respectively.
The value of Δy will be computed thus:
Δy = y(x + Δx) - y(x)
= y(1.1) - y(1)
= 0.5(1.1)⁸ - 0.5(1)⁸
= 0.572
The value of dy will be:
= y'(x)dx
= (0.5)⁸ × x⁷(0.1)
= 0.4 (1)⁷
= 0.4
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