State three shortcomings of polynomial interpolation that, Basic Computer Science

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State three shortcomings of polynomial interpolation that

1. What is a piecewise polynomial?

2. State three shortcomings of polynomial interpolation that are improved upon by piecewise polynomial interpolation.

3. State at least one advantage and one disadvantage of piecewise constant interpolation.

4. State at least two advantages and two disadvantages of broken line interpolation.

5. What is a piecewise cubic Hermite?

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