3. For the following functions on [-1, 1], find their least squares approximations of degree n ≤4, written in the form (4.123). The coefficients (f, P;) can be found by either numerical integration (see Chapter 5) or by using a symbolic integrator such as MAPLE or MATHEMATICA. Also graph the errors f(x) - ln(x) on [−1, 1]. (a) f(x)=sin(x); (b) f(x) = log(1+x²); f(x) = tan¯¹x; (c) (d) f(x) = e', t = ½ (x + 1); (e) f(x) = f(x) = cos [¼л (x + 1)]. π