Question 3

Durée : 5 mn

Note maximale : 6

Question

Calculer une "approximation précise" de :

  • \(a.~~u = \sqrt{3+0,1}\)

  • \(b.~~v = \ln(1-10^{-2})\)

  • \(c.~~w = \tan(45° - 1')\)

Solution

Appliquons les formules précédentes :

  1. \(u=\sqrt{3+0,1}\cong 3+\frac{0,1}{2\sqrt 3}\)

    \(\color{blue}u \# 1,761~~\color{red}\textrm{(2 points)}\)

  2. \(v=\ln(1-10^{-2})\cong\ln 1+(-\frac{10^{-2}}{1})\)

    \(\color{blue}v \# - 10^{-2} ~~\color{red}\textrm{(2 points)}\)

  3. \(w=\tan(45°-1')\cong\tan 45°+(1+\tan^245)(-\frac{\pi}{180\times 60})\)

    \(~~\#1-2(2,9.10^{-4})\)

    \(\color{blue}w \# 0,99942~~\color{red}\textrm{(2 points)}\)