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Solutions must include In teh following problems assume UD is the unit digit and TD...

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Algebra

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Solutions must include In teh following problems assume UD is the unit digit and TD is the tens digit of the Student ID c 1 1 0 1 c d is the remainder of dividing UD by 3 then increased by 1 p is the remainder of dividing UD TD by 3 then increased by 2 q is the remainder of dividing UD by 4 then increased by 3 43 3 4 Duration 2h PROBLEM 1 Compute and mark on the complex plane 3p 8 cos 347 8 sin 347 PROBLEM 2 sary comments and calculations 10p Find solution of a system of linear equations 3p verify if A is a basis of R 3p find a basis and the dimension of span A PROBLEM 4 Pind values with variables 21 22 23 24R PROBLEM 3 For a tuple of vectors A 3p p 3p 2p 3 1 p 3 2p 1 1 p 1 in 3p Him 1 3 gn 4p im 9 1 m 2 PROBLEM 5 is continuous at x 0 PROBLEM 6 For a function f x 34 d 340 2 3 1 x 2d 2 d 40 es des 1 1 2 de 3p the roots of w z 2 1 3 4 2 21 22 25 2x4 1 CX140X20 1 1 1 cx 0 1 x2 0 3 x3 20 1 4 0 5 x2 2x3 24 5 4p verify if p 7 p 1 2p 5 span A 3p lim are ty wpx 10p Find parameters a beR for which a function f x a arcsin cos b 3p find the left slant asimptote 5p examine the monotonicity and find local extreme values 9 29x 9 2 Points 60 sin px In 1 px for x 0 for x 1 for x 1

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