(a) (i) Use the linear approximation formula or y ~ f'() f(x+x) f(x) + f'(x) Ax with f(x)= e to show that etan (1) sec(x) for small values of z. (ii) Use the result obtained in part (a) above to approximate */12 */ etan(2) da. (iii) Approximate 1/2 etan (2) dx using Simpson's rule with n = 4 strips. How does the approximate answer in (iii) compare with the approximate answer in (ii)? (b) The period of a pendulum of length L is given by T = 2 where g is acceler- 2 ation due to gravity. (i) Use the linear approximation formula given above (in part a(i)) to show that if the length of the pendulum increases by AL then the increase in the period is T AT 2L (ii) Give the percentage change in the period, if the length of the pendulum increases by 4%. -AL.