Math Problem Statement
Given the function ex2 ,discuss briefly about its numerical approximation at point x=0 by a computer using the order 2 and 3 terms of the Taylor series expansion,give the approximation error if 0<x<1
Solution
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Math Problem Analysis
Mathematical Concepts
Taylor Series
Exponential Functions
Numerical Approximation
Formulas
e^(x^2) = 1 + x^2 + (x^4)/2 + (x^6)/6 + ...
Order 2 Approximation: e^(x^2) ≈ 1 + x^2
Error Term: E(x) ≈ (x^4)/2
Theorems
Taylor Series Expansion
Suitable Grade Level
Grades 11-12 or College Level