sol for exam 2 take home

sol for exam 2 take home - Math 116 CALCULUS II SOLUTION...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 116 CALCULUS II SOLUTION FOR MIDTERM EXAM – II (Take-home; 11/14) November 19 (Tue), 2013 Instructor: Yasuyuki Kachi Line #: 23590. [I] (Take-home; 10pts) (a) f ( x ) = m s n =0 f ( n ) ( 0 ) n ! x n + i x t =0 f ( m +1) p x - t P m ! t m dt. (b) If lim m -→ i x t =0 f ( m +1) p x - t P m ! t m dt = 0 , then f ( x ) = s n =0 f ( n ) ( 0 ) n ! x n . This is identical to “Review of Lectures – XX”, page 10, Exercise. [II] (Take-home; 10pts) Madam Rich has recently received a letter from the President and CEO of The University X, her alma mater. It goes: Dear Madam Rich, We are so pround of you as being the most prominent alumna of The University X. Could you please help us by donating us some money. We will proudly name our new football stadium “Madam Rich Stadium”. Please agree to sign the enclosed sheet. Sincerely yours, *** , President & CEO of The University X 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
a Enclosed sheet A I, Madam Rich, hereby agree to consecutively pay to The University X, exactly as dictated by the payment schedule below. I agree that, on each payment, the amount will be automatically deducted from my bank account, with account number xxx, and it will be automatically transferred to The University X account. Payment Schedule A. The amount of payment on the payment # n is exactly one n -th of a dollar p = $ 1 n P . ( See Table 1. ) B. As for the timing of payments, the interval between two consecutive payments is exactly one half of the previous interval. ( See Table 2. ) C. The payment will conclude 48 hours after the payment # 1, but not before. payment # v v v v amount #1 v v v v v v v v $ 1 #2 v v v v v v v v $ 1 / 2 #3 v v v v v v v v $ 1 / 3 #4 v v v v v v v v $ 1 / 4 #5 v v v v v v v v $ 1 / 5 #6 v v v v v v v v $ 1 / 6 #7 v v v v v v v v $ 1 / 7 . . . . . . Table 1. 2
Image of page 2
payment # v v v v timing of payment #1 v v v v v v v v −− #2 v v v v v v v v 24 hours after payment #1 #3 v v v v v v v v 24/2 hours after payment #2 #4 v v v v v v v v 24/4 hours after payment #3 #5 v v v v v v v v 24/8 hours after payment #4 #6 v v v v v v v v 24/16 hours after payment #5 #7 v v v v v v v v 24/32 hours after payment #6 . . . . . . Table 2. Suppose you are Madam Rich’s fnancial advisor. Your job is not to let her lose all her money. Should you tell her that it is okay to sign? Explain. b Answer B : Observe the Football series 24 2 0 + 24 2 1 + 24 2 2 + 24 2 3 + 24 2 4 + 24 2 5 + 24 2 6 + ··· = 48.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern