[4} Consider the function J{(ch) = x5 cos x. [i] Find the linear approximation L to the function f at a = E. {ii} Graph f and L on the same set of axes. [iii] Based on the graphs of part [ii], state whether linear approximations to f near a are underestimates or overestimates. [iv] Compute f\"(a) to conrm your conclusion. [5] Use linear approximations to estimate the following quantities. Choose a suitable function f and a value of a that produces a small error. [i] V4.97 [in e 0.02 [6} Differentials. Consider the function f(x) = ln(1 x). [i] Express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. [ii] Use your answer in part [i] to approximate the change inf when 3: changes from x = 1 tox = 1.02