1.a) Evaluate the following limit:
lim {1-cos(x2)} / 4x4, as x-> 0
b) f(x) = {ln(sin(x))}2, find f'(x).
2. a) Given that a differentiable function y is given implicitly by
sqrt(xy) = cos(x+y)
find an expression for y', the derivative of y.
b) Let f(x) = x3 - 6. Use the starting value xo = 2 and three iterates, namely, x1, x2, x3
along with Newton's method to estimate the root of the equation x3 - 6 = 0.
3. a) Find the derivative of the function f(x) = xx+2
b) Find the derivative of the function g(x) = e3x cos(sin(x))