Find the approximate value of ³√0.99 up to 4 decimal places.
Let b3=0.99. Also, let us assume that a=1 an ϵ be a small correction factor such that b=a-ϵ.
Now, cubing both sides:
b3=a3-3a2ϵ+3aϵ2-ϵ3
0.99=1−3ϵ+3ϵ2−ϵ30.99=1-3ϵ+3ϵ^2-ϵ^30.99=1−3ϵ+3ϵ2−ϵ3
Assuming that ϵ3<<ϵ2<<ϵ :
0.99=1−3ε0.99=1-3\varepsilon0.99=1−3ε
ε=(1−099)/3=0.0033\varepsilon=(1-099)/3=0.0033ε=(1−099)/3=0.0033
0.993=1−0.0033=0.9967\sqrt[3]{0.99}=1-0.0033=0.996730.99=1−0.0033=0.9967
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment