Math Problem Statement

Compute T2(x) at x=0.5 for y=ex and use a calculator to compute the error |ex−T2(x)| at x=1.5 .

Solution

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Math Problem Analysis

Mathematical Concepts

Taylor Series
Exponential Function
Error Estimation

Formulas

T2(x) = f(0) + f'(0) * x + (f''(0)/2) * x^2
Error = |e^x - T2(x)|

Theorems

Taylor's Theorem

Suitable Grade Level

Grades 10-12