{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Practice Test 2a - a n 1 = √ 3 a n 4 a 1 = 5 Is this...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Practice Test II A for Calculus I, Math 1501, September 19, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Write answers in boxes where provided. Provide exact answers; not decimal approximations! For example, if you mean 2 do not write 1 . 414 . . . .
Image of page 1

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

View Full Document Right Arrow Icon
I: (25 points, No partial credit) a) True or false: The equation x 1 / 3 - x + 4 = 0 has a solution in [0 , 8]. b) True or false: The function f ( x ) = 1 1+ x 2 defined on [0 , ) has an inverse function. c) True or false: If lim n →∞ ( a n + b n ) exists and if lim n →∞ a n exists then lim n →∞ b n exists too. d) Tue or false: For every positive integer p lim n →∞ log( n ) n 1 /p = 0 e) Using e a 1 + a , valid for all a , derive an anlogous inequality for the log function.
Image of page 2
II: (25 points) Which of the following limits exist? Compute them if they exist. Otherwise explain why they do not exist. a ) lim n →∞ ( n + 1) 2 - n 2 3 n + 5 b ) lim n →∞ ( p n 2 + n - n ) c ) lim n →∞ n (sin( 1 n )) 2 d ) lim n →∞ (1 - sin( 1 n )) n e ) lim n →∞ (cos( 1 n )) n
Image of page 3

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

View Full Document Right Arrow Icon
III: (25 points) Consider the sequence, given recursively by
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a n +1 = √ 3 a n + 4 , a 1 = 5 . Is this sequence convergent? If yes calculate the limit. Proceed along the steps outlined below a) Is this sequence bounded above or below? b) Is this sequence monotone increasing or decreasing? c) Calculate the limit c . d) For which values of n is | c-a n | < 10-6 ? IV: (25 points) Suppose you buy a car and you get a loan over P = $5000 .-at an interest rate of 5%, monthly compounded. Suppose that you want to pay back the loan within 3 years with Fxed monthly payments. How big is your monthly payment? ±ill in the following steps: a) Denote the monthly payment by M and set a = 5 / 100. How much do you owe at the end of the Frst month (i.e. after your Frst payment)? b) How much do you owe after the n-th month? c) Calculate your monthly payment from the answer in b) (Here you may use a calculator)....
View Full 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