\fQuestion 1. If values of a are restricted to values closed to the point of tangency, the y-values of the tangent line are reasonably close to the y-vales of the curve. This means that the equation of the tangent can be used to approximate the equation of the curve. This is called a tangent line approximation (a) Determine the equation of the line tangent to y = 4 sin x cos(2x) when x = 5 6 7 (b) Use tangent line approximation to estimate the value of y = 4 sin x cos(2x) when x = 2.5 (c) Calculate the value of y = 4 sin & cos(2x) when x = 2.5 Question 2. Determine algebraically the absolute maximum and minimum values of f(a) = sina(1 - cos a) on the interval [0, 27] Question 3. (a) If f(x) = (sec x + tan x), show that (i) f'(x) = 2f(x) sec x (ii) f" (ze) = f' (x) (2 sec x + tan x) (b) If f(x) = (sec x + tan x)", n E R,n > 0, show that (i) f' (x) = nf(x) sec x (ii) f" () = f'(x) (n sec x + tan x) (c) Is the result from part b) true if n