Science:Math Exam Resources/Courses/MATH110/April 2017/Question 07 (b)
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Question 07 (b) |
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Consider the function
where is a constant. For what value of is continuous on its domain? Provide justifications |
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 |
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First, we know that fundamental functions are continuous on its domain, e.g. exponential functions, trigonometric functions, and in our case polynomials. Then for piecewise function which is composed of several polynomials, we only need to consider its continuity at end points, more precisely, points connecting two polynomials. Recall that continuity means left limit is equal to right limit, and also equal to the value at that point. |
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.
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Solution |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. According to analysis in the hint, let's first find its left limit, right limit, and value at point , then and also note that has value at point since the domain contains , so Now in order to make sure is continuous at this point, we need Therefore, . |