We want to apply the Lagrange Error Bound Theorem, and bound it to 0.001: For those unknowns variables in the theorem, we know that: The

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In order to compute the error bound, follow these steps: Step 1: Compute the ( n + 1 ) th (n+1)^\text{th} ( n + 1 ) th derivative of f ( x ) . f(x). f ( x ) . Step 2: Find the upper bound on f ( n

When x is 1.45 is going to be less than or equal to the absolute value, our M is e squared, e squared over, over n plus one factorial times 1.45, that's our x that we care about, that's where we're calculating the error, we're trying to bound the error, minus where we're centered, minus

Computing each of T (π/4) and cos (π/4) to eight digits of accuracy: The actual error is: 0.70742921 – 0.70710678 = 0.00032243. This is much better than our estimated

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