Practice question · Select all that apply
Select every TRUE statement about Taylor approximation.
Hints
- One option would make the whole subject of error bounds unnecessary.
- Could a polynomial of degree 3 equal the exponential function everywhere?
Show the answer
- A. The approximation is most accurate near the centre a
- B. Adding more terms generally improves accuracy
- C. A Maclaurin series is a Taylor series centred at a = 0
- E. The linear approximation is the tangent line at a
Why
Taylor approximation is fundamentally LOCAL: accurate near a, degrading as the distance grows, improvable by more terms but never exact for a finite polynomial. The exponential grows faster than any polynomial, so no truncation can match it everywhere.
Practise Taylor Approximation
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