Derive the Rayleigh-Jeans approximation from Planck's function. Start by expanding the exponential term in the Planck's function (exp (hc/kBT)) into a Taylor series and discard quadratic and higher-order terms. When is it safe to discard these terms (brief mathematical justification)? [2 pt] (b) For the case that T = 300 K, determine the error that you commit by using the Rayleigh-Jeans approximation instead of Planck's function for the wavelengths of 500 nm, 50 m, and 1 mm