A obtain a linear approximation for y at average laboratory

Question

With appropriate assumptions the number of moles of oxygen in a fixed volume of air is given by the formula Y = 0.336xdxz, where Y =moles of oxygen, x₁ =atmospheric pressure (centimeters of mercury). and x₂ = atmospheric temperature (degrees Kelvin). Suppose that average laboratory conditions are x₁₀ = 76.0 centimeters of mercury and x₂₀ = 295 K.

(a) Obtain a linear approximation for Y at average laboratory conditions.

(b) Assuming σ₁ = 0.2 cm and σ₂ = 0.5 K, check the linearity assumption over the ranges x₁ ± 3σ₁ and x₂ ± 3σ₂.

(c) Obtain an approximate value for the standard deviation of Y at average laboratory conditions.