Let S5(x) represent the continuous least-squares trigonometric polynomial of degree 5 for f(x) = -x on [-, π]. Let further I(u) be I(u) = f e-x² S5(x) tanh(sinh-¹(x)) dx. If, for a certain value of u, I is approximated using the Trapezoidal rule as -0.015, then approximate that value of u by using Newton's method with an initial approximation of such that the relative error between two iteration steps is less than 10-6.

Evaluate 3 dz 2

2 dz 8

Let AABC be a triangle. Fix the points X, Y, and Z on AB, AC, and BC, respectively (as in the figure) such that BX = - = CZ AY = 4. Assume that the area of AXYZ is one and calculate the area of AABC. ХА YC ZB