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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
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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.
(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
(b) Solve the differential equation y′^ = 2xy + ex^2 ; y(0) = 2
(b) ∑∞ n=1 en−^1 n 2
(b) Verify that f (x) = ∑∞ n=0 anxn^ solves the differential equation f ′′^ − 2 xf ′^ + f = 0 .
