Use the linear approximation to estimate the change in

Question

1. Use Nekton's method and the function f(x) = xⁿ - a to show that the general rule for approximating x = ⁿ√a is {(n - 1) x_nⁿ + a} / nx_n^n-1.

2. Use the linear approximation to estimate the change in volume of a right circular cone of fixed height h = 4m when its radius increases from r = 3m to r = 3.05m [v(r) = πr²h/3].

3. Find two positive numbers x and y such that "The sum of the First number squared and the Second number is 54 and the product of x and y is as large as possible.