Consider the Taylor series expansion for cos(x) and e\' at 0 are given in the fo

Question

Consider the Taylor series expansion for cos(x) and e' at 0 are given in the followings Taylor series expansion up to only the first non- cos(x) l Eq. zero term Taylor series expansion up to the third non-zero cos(x) Eq (2) Taylor series expansion up to only the first non- zero term Taylor series expansion up to the third non-zero Eq. (4) 21 For error estimation, Use the following relation, Emor Exact Function- Approximated Function x 100(%) Exact Function a) What is the error, in when you approximate cos(x) using Taylor series expansion, i e., Eq. (see above) at r 0.1 (in radian)? b) Repeat part (a) using Eq. (2) (see above) atx 0.1 (in radian). Please compare the errors between parts (a) and (b) and provide the reason why you have different level of error. c) What is the error, in ee, when you approximate e function using Taylor series expansion, i e Eq. G see above) at r 0.1? part (c) nd (d) and provide the reason why we have different level of error.

Explanation / Answer

a) Exact function = cos 0.1 = 0.995

Approxiated function = 1

Error = |0.995 - 1| / 0.995 * 100 = 0.5025%

b) Exact = 0.995

Approxiated function = 0.995004

Error = |0.995 - 0.995004| / 0.995 * 100 = 0.0004020%

c) Exact = 1.105171

Approximated function = 1

  Error = |1.105171 - 1| / 1.105171 * 100 = 9.516%

d) Exact = 1.105171

Approximated function = 1.105

  Error = |1.105171 - 1.105| / 1.105171 * 100 = 0.0154%

  

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