Solved by verified expert:We have done a lot of work in the land of Calculus but because of the nature of the course, we have not had the opportunity to provide a full view of the major theorems we have discussed. Many of the results we have proved in class and utilized through examples have rich histories of brilliant mathematicians and ingenious ideas that are not immediately clear when you see just the statement. The first writing assignment will be topick and further examine the history, the proof, and the many uses of one of these immaculate theorems or ideas.Instructions: Here is a list of suitable results, ideas, and theorems. You should pick the one that interests you the most.The IntermediateValue TheoremFermat’s TheoremThe Extreme Value TheoremRolle’s TheoremThe Mean Value TheoremL’ Hospital’s RuleThe Definition of the Derivative*The Precise Definition of a Limit*The Linear Approximation Formula (Taylor Expansion?)*or if you have any other result you are interested in you are welcome to email me to ask for approval.Write a short (3-4page) paper in which you answer the following questions:1.) What is the statement of the Theorem/Idea/ Result? Is there a particular mathematician that first proved this? Is there a story concerning the development of the result?When was this result first utilized? What was the problem that was being solved?2.) Give a full proof of the result. At each step of the proof you must justify in words why you are able to conclude such. DO NOT COPY AND PASTE THE PROOF FROM AN ONLINE SOURCE! You may use your notes and your textbook to help but you still need to describe each step.* For these there is no one proof to prove. If you choose any of these ideas then you need to prove two of the resulting theorems using this idea (for example, if you choose the definition of derivative you may choose to prove the sum rule and the constant multiple rule).3.) Set up and solve 4problems that use the theorem or result. Each of these problems must be different in structure. In other words, YOU MAY NOT SIMPLY CHANGE THE NUMBERS OF THE PROBLEM! You can include a word problem as a distinct problem and I will consider a standard word problem and related rates problem as being different if these are applicable to the result you chose.4.) Conclude by stating the importance of your chosen results and describe the areas outside of math where this result may be applied (There are plenty of these but you may have to be creative in how you search for them).

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