onsider the following function. F(2) = [*d (a) Use the Maclaurin expansion for e- to express the function F(x) as an alternating power series in x. Your work must include using the Maclaurin series for e to create a series for e-t and then integration from 0 to x. Σ F(x) = n = 0 (b) Find an N such that the partial sum SN of the Maclaurin series approximates the integral for x = 1.5 to within an error of at most 0.001. Work must including using the alternating remainder theorem to find the partial sum N and the error term N+1. N = (c) Compute Sy using the N found above. (Round your answer to six decimal places.) SN =

Q: Need questions 4 5 and 6 answered please

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A: We find linear function using table and then find f(0).

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A: I have to answer for part-d and part-e, so i use the previous result .

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A: Step - I: f(n) = 3n2 + 2n - 1         < 3n2 + 2n          ≤ 3n2 + 2n2 for n ≥ 1            = 5n2…

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A: Note: Hey there! Thank you for the question. As per your request, we have solved the first three for…

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A: The given series is ∑n=1∞x-3nn25n. Let an=x-3nn25n, then an+1=x-3n+1n+125n+1. Apply ratio test,…

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A: The solution is given below :

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.