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Image text transcribed for accessibility: In this problem we examine the importance of Re son of Convergence (ROC) that associates the form of the Laplace transform to the time characteristics of a signal. Consider the Laplace Transform X(s) = (s + 10)-1 This form is associated with one of two time signals, depending on whether s is evaluated in the ROC with real(s)<-10 or real(s) >-10: Within either ROC, the actual value of real(j) doesn't matter. To demonstrate this, we evaluate the inverse Laplace transform, approximately, and show that it converges to one of the signals above. Specifically, you are to implement the following, approximation: where N is intended to be large. Aw is intended to be small. Calculate the approximations for a time range between -1 and 1 seconds, and choose at least two values of sigma (i.e. real(s)) in the each region of convergence to convince yourself that the value doesn't matter, in the limit as N tends to infinity, and Delta omega tends to zero (the integration limit) Specifically, choose values {1, -1,-12-15}.

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