The Maxwell-Boltzmann probability density function f(v) is given byf(v) = v2exp(-2fJwhere m (kg) is the mass of each molecule, v (m/s) is the speed, T (K) is thetemperature, and k = 1.38 x 10-23 J/K is Boltzmann's constant. The mostprobable speed v P corresponds to the maximum value of f( v) and can bedetermined from d) = 0. Create a symbolic expression for f(v), differentiateit with respect to v and show that vP = . Calculate vP for oxygenmolecules (m = 5.3 x 10-26 kg) at T = 300 K (k = 1.38 x 10-23 J/K). Make aplot of f( v) versus v for 0 v 2500 m/s for oxygen molecules

Lecture 2- Johnson Factor: o x + 6x + 8 (x+4)(x+2) 2 o x – 64 (x+8)(x-8) o x – 5x -14 (x-7)(x-2) o 4x – 100 4(x – 25) 4(x-5)(x+5) Difference and Sum of Perfect Cubes (S.O.A.P) 3 3 2 2 o A – B = (A – B) (A + AB + B ) x -64 (x-4)(x + 4x +16) o A + B = (A + B)(A - AB + B ) 2 x – 1 (x+1)(x -x+1) 3 What can you exclude from the domain of x x ≠ 0 3x o x−2 ,x ≠ 2 9x ,x≠3,−6 o x +3x−18 Simplify 2 (x+1 )x−1 ) x −1 → →x≠−1→ x−1 o x +2x+1 (x+1 )x+1 ) x+1 x+3 x