Question B: i) If you do a first-order Taylor approximation to sin(x) at x=pi/4,
ID: 2828889 • Letter: Q
Question
Question B: i) If you do a first-order Taylor approximation to sin(x) at x=pi/4, will your results be an upper bound or lower bound (or neither) on sin(x) for values of x close to pi/4 ? ii) If you do a 2nd-order Maclaurin approximation to cos(x), will you get a UB or LB or neither for x values close to 0? iii) If you do a 3rd-order Maclaurin approx. to exp(x), will you get a UB or LB or neither for x values close to 0? iv) If you do a first-order Taylor approx. to log(x) at x=1, will you get a UB or LB or neither for x values close to 1?
Explanation / Answer
Upper bound because it is alternating series
Lower bound because it is an alternating series.
Neither because it is not alternating.
Upper bound because it is alternating.