Science:Math Exam Resources/Courses/MATH100/December 2011/Question 04 (b)
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Question 04 (b) 

FullSolution Problem. Justify your answers and show all your work. Simplification of answers is not required unless explicitly stated. Let be the second degree Taylor polynomial about for Is larger than ? Please justify your answer. 
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 

What can you say about the error between the Taylor polynomial and the actual function? That error is also called the remained. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Lagrange's Remainder Formula states that: Where is a number in When is positive, then is an underestimate; if it is negative, then is an overestimate. For this problem, Since and are both positive, we can conclude that is also positive since the factorial is positive as well. This means that: 