Science:Math Exam Resources/Courses/MATH215/December 2011/Question 05 (c)
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Question 05 (c) 

Let f and g be two functions satisfying the following conditions where F(s) and G(s) are the Laplace transforms of the functions f(t) and g(t), respectively. Find the value of g(5). 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

How can we use the identity to our advantage? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From the chart at the end of the exam we have the following identity and we should always consider this identity first if we see products of polynomials and transforms. Comparing this to what we have, we see that since and then Therefore we have We now need to compute . Returning again to our chart we have the identity where u_c is the Heaviside function defined as Using this identity, we can immediately write Therefore we have that 