Question

Calculus Problem, l'Hopital rule.

Please see the attached picture.

I know the function is undetermined with the limitation of 0+, but even after I have applied l'hopital rule to derivative the numerator and denominator, I still find the function is undetermined as the λ always has a negative power, so I cannot substitute λ=0 into the equation.

Please help me. Really appreciated!

A blackbody system is a system that absorbs any radiation it encounters. An example would be a perfectly matte black surface, which only absorbs and does not reflect any radiation. Blackbody systems emit blackbody radiation The Rayleigh-Jeans Law (late 1800's) expresses the energy density of blackbody radiation of wavelength A using the following function: 87TKT f(A) Note that A is the independendent variable, T is the temperature in Kelvin, and k 1.38064852 x 10 23 J/K is Boltzmann's constant. The Rayleigh-Jean Law accurately models experimental measurements for long wavelengths but disagrees for short wavelengths. In 1900, Max Planck presented a better model, known as Planck's law: 8πhεA-5 fp(A) hc (exT 1) where h 6.6262 x 1031 Js is Planck's constant, c 2.997925 x 108 m/s is the speed of light, and k C is Boltzmann's constant 1. (10 marks) Use l'Hopital's rule to show that lim f()0 and lim fp(A)= 0 A-0+ This shows that Planck's law is a better approximation than Rayleigh-Jeans Law for short wavelengths and similar information for long wavelengths

Answer 1

You keep on applying l'hopitals rule. I use the change of variable to simplify.

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