I am in no rush to get this done but, if anyone can help with this entire block, I would appreciate it greatly. Thank you so much! STUDENT PROJECTProving that e is IrrationalIn this project, we use the Maclaurin polynomials for e to prove that e is irrational. The proof relies on supposing that e isrational and arriving at a contradiction. Therefore, in the following steps, we suppose e = ris for some integers r and swhere s + 0.1. Write the Maclaurin polynomials po(x), p1(x), P2(x), P3(x), P4(x) for e. Evaluate po(1), P1(1). P2(1), P3(1), P4(1) toestimate e.2. Let R,(x) denote the remainder when using p„(x) to estimate e. Therefore, R,(x) = e* – P„(x), and R,(1) = e - P„(1).Assuming that e =- for integers r and s, evaluate R,(1), R;(1), R,(1), R3(1), R4(1).3. Using the results from part 2, show that for each remainder Ro(1), R1(1), R2(1), R3(1), R4(1), we can find an integer ksuch that kR,(1) is an integer for n = 0, 1, 2, 3, 4.4. Write down the formula for the nth Maclaurin polynomial p,(x) for e* and the corresponding remainder R,(x). Showthat sn!R,(1) is an integer.5. Use Taylor's theorem to write down an explicit formula for R„(1). Conclude that R,(1) # 0, and therefore,sn!R,(1) # 0.6. Use Taylor's theorem to find an estimate on R,(1). Use this estimate combined with the result from part 5 to showsethat sn!R„(1) <;Conclude that if n is large enough, then sn!R,(1) < 1. Therefore, sn!R,(1) is an integer withn+1*magnitude less than 1. Thus, sn!R,(1) = 0. But from part 5, we know that sn!R,(1) # 0. We have arrived at acontradiction, and consequently, the original supposition that e is rational must be false.

Name: I am in no rush to get this done but, if anyone can help with this ent
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Description: I am in no rush to get this done but, if anyone can help with this entire block, I would appreciate it greatly. Thank you so much! STUDENT PROJECTProving that e is IrrationalIn this project, we use the Maclaurin polynomials for e to prove that e is i