已知y=x的三次1,在x=2处计算当△x分别为1,0.1,0.01时的△y及dy之值

Question

已知y=x的三次_1,在x=2处计算当△x分别为1,0.1,0.01时的△y及dy之值

Answer 1

y=x³-1
Δy=(2+Δx)³-1-(8-1)=3*2²Δx+3*2*Δ²x+Δ³x
Δx=1,Δy=(2+1)³-1-（2³-1）=19
Δx=0.1,Δy=(2+0.1)³-1-(2³-1)=1.261
Δx=0.01,Δy=(2+0.01)³-1-(2³-1)=0.1206

Δy=(x+Δx)³-1-(x³-1)=3*x²Δx+3*x*Δ²x+Δ³x
Δx-->0,
dy=3x²dx

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