6. Find Maclaurin series for $F(x) = \int_0^x \sqrt{t}e^t dt$ and use it to evaluate $F(1)$ to an accuracy of 3 decimal places. (Note: $6! = 720$, $7! = 5040$)
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The Maclaurin series for a function F(x) is given by the formula: F(x) = F(0) + F'(0)x + (F''(0)x^2)/2! + (F'''(0)x^3)/3! + ... In this case, F(x) = redt. Let's find the derivatives of F(x) and evaluate them at x = 0. F'(x) = d(redt)/dx = redt * d/dx = redt * Show more…
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