Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 02
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Question 02 

Find the value of the constant that makes continuous, where 
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 

This is a piecewise function, what needs to happen at the boundary of the pieces for a piecewise function to be continuous? 
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. The two parts of are continuous, so we only need to make sure that is continuous at . That is . Again, since both parts are continuous this equality will be achieved if the two parts are equal. We set , and solve for : Therefore, makes continuous. 