The images havent been loading all week for me so you have to go to the instruct

Question

The images havent been loading all week for me so you have to go to the instructors page that he has the post on its #2 that I want solved if you dont feel comfortable going to the website I can send the question via email I have a final tomorrow very critical I get these answered. this is the link a pdf should open.....http://markrobrien.com/ExamFinalPracSummer13.pdf

The images havent been loading all week for me so you have to go to the instructors page that he has the post on its #2 that I want solved if you dont feel comfortable going to the website I can send the question via email I have a final tomorrow very critical I get these answered. this is the link a pdf should Estimate 0 1 e -x2 dx with an error of 1/100.

Explanation / Answer

First find Taylor series for e^(-x^2).

Recall that e^u = 1 + u + (u^2)/2! + (u^3)/3! + ...

now substitute u = -x^2:

e^(-x^2) = 1 - x^2 + (1/2)x^4 - (1/6)x^6 + (1/24)x^4 + ...

now integrate the polynomial term by term:

x - (1/3)x^3 + (1/10)x^5 - (1/42)x^7 + (1/120)x^5

now evaluate between 0 and 1:

1 - 1/3 + 1/10 - 1/42 = 0.74285714285

becuase this is an alternating series, the error is no bigger than the
absolute value of the next term, which is 1/120 < 1/100

so your answer is: 0.74

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.