Science:Math Exam Resources/Courses/MATH104/December 2015/Question 03 (b)
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Question 03 (b) |
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Find the value of for which the function is continuous for all |
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. |
Hint 1 |
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Recall that for a function to be continuous at , we need In particular, the aforementioned limit must exist. |
Hint 2 |
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Consider the continuity of at Clearly, is defined there (what is its value?). What are and ? |
Hint 3 |
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Recall that if and only if and exist and are equal to |
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. Clearly is continuous for all For to be continuous at , we need We immediately observe that Now while For to exist, we must have , in which case this common value will be the value of the limit. This same value of will also guarantee that is continuous at , since Solving for , we have |