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)

Sawyer is studying diffraction. he draws a diagram of a plane wave to show how light waves travel. which best describes sawyer’s error? the wave fronts should be perpendicular to the direction in which the waves move. the arrow showing the direction of movement of the waves should be pointing to the left. the arrow showing the direction of movement of the waves should be pointing downward. the wave fronts should be both parallel and perpendicular to the direction in which the waves move.

Electromagnetic induction. a coil of wire contains n turns and has an electrical resistance r. the radius of each turn is a. initially, inside the coil there exists a uniform magnetic field of magnitude b0 parallel to the axis of the coil. the magnetic field is then reduced slowly. the current induced in the coil is i. how long does it take for the magnitude of the uniform field to drop to zero?

What is the rate of 12 liters of water moving through a water hose in 4.0 minutes?