I prepare the handwriting. Please solve it asap and send to me.Also, Please solve it from back. thank you.Math 108 – Exam # 3 – Fall 2020

You may use your textbook and your class notes during the exam.
You need to follow the notation used in our textbook and in our class notes.
You may not use the internet, a smart device (cellphone, watch, etc.), any apps or other resources
to find solutions. Using any of those resources will result in a 0 on the exam and a report of cheating
will be filed with the college.
You are not allowed to collaborate with anyone during the exam.
You must show all work, justify your answers, and write legibly to receive full credit.
A correct answer with unsupported work is an automatic zero on the problem.
You may be selected after the exam to have a private Zoom session with your professor to explain
your work on a problem.
2 −7
Problem 1. Find the inverse Laplace transform of ( ) = 2−2 +6
Problem 2. Find the Laplace transform of ( ) = 3 sin 4
Problem 3. Solve the given initial value problem for y(t) using the method of Laplace transforms.
′′ − ′ = cos
(0) = 0,
′ (0) = 0
Problem 4. Solve the given integral equation for y(t).

( ) + ∫ − ( ) = cos
Problem 5. The graph of a function g(t) is shown below.
a) Express the function in terms of unit step functions. Simplify your answer.
b) Find the Laplace transform of g(t).
Problem 6. The given vector functions are solutions to a system x’(t) = Ax(t). Determine whether they
form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general
1 = [
2 −
2 = [ ] 5

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