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MarcKrishkeMath1540FinalExam

# MarcKrishkeMath1540FinalExam - Math 1540 Final Final Math...

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Math 1540 Final Final Math 1540 Final Exam Name: 1.) Expand the following using the Binomial Theorem. ( 29 ( 29 ( 29 ( 29 ( 29 4 4 3 2 2 3 4 4 3 2 4 3 2 4 3 2 4 4 4 2 3 2 2 (3) 2 (3) 2 (3) (3) 1 2 3 4! 4! 4! 16 8 (3) 4 9 2 (27) 81 1!3! 2!2! 3!1! 16 4 (24) 6 36 4 (54) 81 16 96 216 216 81 y y y y y y y y y y y y y y y y y       - = - + - +             = - + ⋅ - + = - ⋅ + ⋅ - ⋅ + = - + - + 2.) Find a formula for the nth term, n a , for the following: The eighth term of an arithmetic sequence is 75, and the twentieth is 39. The nth term of an arithmetic sequence is 1 ( 1) n a a d n = + - Then 8 1 20 1 (8 1) 75 (20 1) 39 a a d a a d = + - = = + - = 1 1 7 75 (1) 19 39 a d a d + = + = 1 1 7 75 1( 19 ) ( 1)39 a d a d + = - + = - 1 1 7 75 19 39 12 36 3 a d a d add d d + = - - = - - = = -

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Math 1540 Final Final From the equation (1) 1 1 1 1 7( 3) 75 21 75 75 21 96 a a a a + - = - = = + = Thus, | 96 ( 3)( 1) 96 3 3 99 3 n n n a n a n a n = + - - = - + = - 3.) Solve the system using Gaussian elimination to obtain RREF. Show all work. 2 3 4 2 4 3 2 3 x y z x y z x y z - - = - + + = - + - = 1 2 2 1 3 3 2 3 2 1 2 3 4 1 2 3 4 1 2 3 4 1 2 4 3 0 0 1 1 0 5 5 5 2 1 1 3 0 5 5 5 0 0 1 1 R R R R R R R R + - - - - - - - - - - - - - - 2 3 2 3 2 1 5 1 2 3 4 1 2 3 4 0 1 1 1 0 1 0 2 0 0 1 1 0 0 1 1 R R R R R - - - - - - - - 1 2 3 1 2 3 1 0 0 3 0 1 0 2 0 0 1 1 R R R R + + - Answer: The solution set is {(3, –2, 1)}. 4.) Find the Partial fraction decomposition for the following: 2 2 ( 5) ( 5) ( 5)( 1) 1 5 4 5 5 5 x x x x A B x x x x x x x x x x x x = = = = + + - + + - - + + - + - -
Math 1540 Final Final A(x + 5) + B(x – 1) = x Ax + 5A + Bx – B = x (A + B)x + 5A – B = x 1 1 1 6 5 0 6 1 1 1 1 6 6 1 5 1 6 6 A B A B A A B A A B A A B B + = + = = - = = + = = = + = = Thus, 2 1 5 6 6 1 5 4 5 x x x x x = + - + + - or 2 1 5 6( 1) 6( 5) 4 5 x x x x x = + - + + - 5.) Graph the following piece-wise function. 2

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MarcKrishkeMath1540FinalExam - Math 1540 Final Final Math...

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