Science:Math Exam Resources/Courses/MATH110/December 2015/Question 03 (a)
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Question 03 (a) 

Consider the following function,
where and are constants. (a) Find values of and for which is continuous everywhere. 
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 

A function is continuous at a point if if satisfies

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. Recall that exponential functions and polynomials are continuous on the whole real line,. Therefore, it is enough to consider the continuity of function at and .
and , to have the continuity at , we need .
and . This implies that is continuous at when . i.e., .
