Quiz 2 Solutions.pdf - MC1 The first multiple choice...

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MC1 The first multiple choice question asked you which of four functions of s arose as the Laplace transform of a polynomial. Two of the choices were sums of terms of the form a 1 s n for some real number a and n 1. Such a term is the Laplace transform of a monomial, so a sum of such terms is the Laplace transform of a polynomial. That ruled out those two possibilities. One of the choices was a rational function in s . However, the numerator was a factor of the denominator and it simplified to something of the form a 1 s n and was hence the Laplace transform of a polynomial. The final option had a constant 1, which is the Laplace transform of δ ( t ), which is decidedly not a polynomial. The answer was that one. MC2 In this one, you were asked to find the function to which cos ( nπx m ) was not orthogonal on some symmetric interval. One of the choices was of the form ax 3 which is odd. Since the cosine function is even, their product is odd, so the integral on a symmetric interval is 0. So the answer was not ax 3 . For the other three options, if you changed all of them to have a denominator (inside the trig function) equal to L , you would see that they are orthogonal (this is the list in class). The correct answer was actually the function you were given but in disguise. A function is not orthogonal to itself unless it is identically 0.