Question B: i) If you do a first-order Taylor approximation to sin(x) at x=pi/4,

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.

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