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test 1 practice

# test 1 practice - ∑ ∞ = 1 300 1 n n n McMaster...

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Math1XX3, Winter 2007 1. [6 marks] Find the solution to the differential equation ) 2 sin( 6 2 x y dx dy = with the condition that 6 / 1 ) 0 ( = y 2. [6 marks] Find the most general solution to the linear differential equation x y y x 1 6 = + McMaster University Page 1 of 10

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Math1XX3, Winter 2007 3. [6 marks] Match the differential equation to the direction field (place he letter of the appropriate direction field in the space provided) i) 2 - + = x y y Field:__B ___ ii) 4 / 3 y y = Field:__A ___ iii) 2 / 2 x e y - = Field:__C ___ iv) xy y = Field:__D ___ McMaster University Page 2 of 10 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 A B C D
Math1XX3, Winter 2007 4. [13 marks] a) Determine if this sum converges or diverges, and if it converges, find the total. 90 – 60 + 40 – 80/3 + 160/9 … b) Determine if this sum converges or diverges, and if it converges, find the total.

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Unformatted text preview: ∑ ∞ = + + 1 300 1 n n n McMaster University Page 3 of 10 Math1XX3, Winter 2007 c) Determine if this sequence converges or diverges. If it converges, find the limit n e a n n ) 3 ln( 2 + = d) Consider the sequence given by n e n e n a-= Is the sequence monotonically decreasing, increasing, or not monotonic? Is it bounded? McMaster University Page 4 of 10 Math1XX3, Winter 2007 5. [8 marks] In each of the following, determine if the improper integral converges or diverges, and if it converges, determine its value. a) dx xe x ∫ +∞-2 b) dx x ∫-2 3 / 5 ) 1 ( 1 McMaster University Page 5 of 10...
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test 1 practice - ∑ ∞ = 1 300 1 n n n McMaster...

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