14.8.1 Function Interpolation

Condition: Use Polin Taylor of the third degree of function \ (f (x) = \ sqrt {x} \) in the vicinity of point 100 to find the approximate value \ (\ sqrt {102} \) and evaluate accuracy. Find both answers in the form of fractions.

At Its Core, Function Interpolation in Numerical Analysis Illuminates The Path Between Known Data Points, Revealing the Behavior of Functions Beond The Confines of the Given Data. Be it Scientific Experiments, Engineering Measurements, Or Financial Records, Real-World Data IS Inherently Incomplete and Scatted. Function Interpolation Comes to the Rescue, Offering Techniques to Construct Approximations that Smoothly Connect the Dots. The Beauty of Function Interpolation Lies in Its Myriad of Methods that Cater to Diverse Scenarios. From Simple Techniques Like Linear Interpolation to More Intricate Approaches Like Polynomial, SPLINE, and Radial Basis Function Interporation, The Toolbox of Methads Adapts to the Complexity of the Data and the Desired Level of Smoothness. Each Method Offers a Unique Way to Stitch Together a Coherent from Disjoint Pieces.