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A unit step function u_c, with c positive, inside a definite integral where the integration goes from 0 to infinity, has only one effect: it changes the integration interval to [c, infinity). 

Fill in the blanks based on the graph below.  No work is required for this problem.   = [one]                          = [two]                            =[dne] =[twotwo]                                        =[three]                            =[neginfin] =[dnetoo]                              =[threethree]                                        =[zero] =[zerotoo]                        Give the equation of any asymptotes found: [yzero]

The Laplace transform of a constant is a constant.

When the civil war between the Scots and English erupts during the reign of Charles I, the rebellion is basically about

OPTIONAL EXTRA CREDIT: Define mental health and identify ONE way to improve it.

Sketch a graph of g(x).  Your graph should include all the information you gave in questions 2-4.  I will be checking your work for this graph.    There is nothing for you to type here, as I will be checking your work to award points. 

A function f is 2 for t < 2 and t for t ≥ 2. What is the unit step function representation of this function?  

Not every function has a Laplace transform.

The quasi-frequency of an underdamped, free harmonic oscillator 

Describe the transformations.  Then state the domain and range.