Let f(x) = ln(x + 1), and x₀ = 1, x₁ = 2, x₂ = 3, and x₃ = 4.
Find the Lagrange form, the Newton form and the standard form of the Lagrange interpolating polynomial L3. Check your answer by veryfying that L3 correctly interpolates f at the given points.
Find an upper bound for the maximum error - L3[1,4] := max 1≤x≤4; f(x) - L3(x)

The intensity of a polarized electromagnetic wave is 12 w/m^2. part a) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=0∘ with the plane of polarization? part b) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=30∘ with the plane of polarization? part c) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=45∘ with the plane of polarization? part d) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=60∘ with the plane of polarization? part e) what will be the intensity after passing through a polarizing filter whose axis makes the angle θ=90∘ with the plane of polarization?

Determine the fraction of the magnitude of kinetic energy lost by a neutron (m1 = 1.01 u) when it collides head-on and elastically with a target particle at rest which is 21h (heavy hydrogen, m = 2.01 u).

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