Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Binomial Series - Mathematics - Exam, Exams of Mathematics

This is the Exam of Mathematics which includes Continuous, Number, Every, Domain, Continuous Functions, Laplace Transforms, Constant, Simplify, Evaluate, Value of the Constant etc. Key important points are: Binomial Series, Incorrect Answers, Simplify, Evaluate, Values, Fraction, Waiting Time, Tributed According, Probability Density Function, Minutes of Ordering

Typology: Exams

2012/2013

Uploaded on 02/21/2013

raja.g
raja.g 🇮🇳

5

(1)

33 documents

1 / 15

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Faculty of Mathematics
University of British Columbia
MATH 121
FINAL EXAM - Winter Term 2009
Time: 12:00-2:30 pm Date: April 24 , 2009.
Family Name: First Name:
I.D. Number: Signature:
Question Mark Out of
1 30
2 20
3 10
4 10
5 10
6 10
7 10
Total 100
THERE ARE 15 PAGES ON THIS TEST. THE LAST 2 PAGES ARE FOR ROUGH WORK, AND
YOU MAY TEAR THEM OFF TO USE. YOU ARE NOT ALLOWED TO USE CALCULATORS,
NOTES OR BOOKS TO AID YOU DURING THE TEST.
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff

Partial preview of the text

Download Binomial Series - Mathematics - Exam and more Exams Mathematics in PDF only on Docsity!

Faculty of Mathematics

University of British Columbia

MATH 121

FINAL EXAM - Winter Term 2009

Time: 12:00-2:30 pm Date: April 24 , 2009.

Family Name: First Name: I.D. Number: Signature:

Question Mark Out of 1 30 2 20 3 10 4 10 5 10 6 10 7 10 Total 100

YOU MAY TEAR THEM OFF TO USE. YOU ARE NOT ALLOWED TO USE CALCULATORS,THERE ARE 15 PAGES ON THIS TEST. THE LAST 2 PAGES ARE FOR ROUGH WORK, AND NOTES OR BOOKS TO AID YOU DURING THE TEST.

  1. Short answer questionscorrect answers in the box, while at most 1 mark will be given for incorrect answers.. Put your answers in the box provided. 3 marks will be given for Unless otherwise stated, simplify your answers as much as possible. (a) Evaluate ∫^ x ln^1 x dx.

(b) For what values of α does ∫^ e∞ x(ln^1 x)α dx converge?

(c) Find f ′(x) where f (x) = ∫^0 x 2 t^2 dt.

(g) Evaluate limn→∞^ ∑nj=1^ j n^23

(h) Estimate the error in approximating e by ∑^5 n=0 n^1!

(i) Evaluate limx→ (^0) (1^ x^2 −^ sin ex^2 2 x (^) ) 2.

(j) Find the midpoint rule approximation to ∫^131 x dx with n = 3.

(c) ∫^ (1−xx (^22) ) 3 / 2 dx (d) ∫^0 π/^3 sin 1 x− 1 dx

  1. (a) Letto obtain the solid R be the region under the curve S. Find the x coordinate ¯ y = √1+^1 xx (^2) of the center of mass offor 0 ≤ x ≤ 1. Revolve RS (^) .around the x axis

(b) Solve the differential equation y′^ = 2xy + ex^2 ; y(0) = 2

  1. Determine if the following series are convergent or divergent. (a) ∑∞ n=1 n 3 n+^2 n

(b) ∑∞ n=1 en−^1 n 2

  1. Define the sequence an recursively by: a 1 = 3 and an+1 = 23 an + (^3) a^4 n. (a) Show that 2 ≤ an ≤ 3 for all n. (b) Prove that {an} converges and evaluate the limit.

(b) Verify that f (x) = ∑∞ n=0 anxn^ solves the differential equation f ′′^ − 2 xf ′^ + f = 0 .

FOR ROUGH WORK ONLY...