The approximate value of E is based on the knowledge of higher numbers

The approximate value of E is based on the knowledge of higher numbers

Because e is about 2.718, which is close to 3, √ 3 is about 1.732
√e=√(3-(3-e))=√3*(1-(3-e)/3)^(1/2)
=√3*(1-(1/2)*(3-e)/3+1/8*{(3-e)/3}^2+.
=1.732*(1-0.047+0.001)=1.732*0.954=1.6523

Approximate value of ln0.99, knowledge of differential of higher numbers

The Taylor expansion formula is used
When (- 1

Use differential to find the approximate value of 3 times √ 8.1

Let y = -; 8.1
After differentiation, Dy = 1 / 3 * 8.1 ^ (- 2 / 3) DX
Then y ≈ & # 8731; 8 + 1 / 3 * 8 ^ (- 2 / 3) * 0.1 = 0.25 * 0.1 / 3 = 2 + 0.0083 = 2.0083