MATH110 April 2018
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q7 (e) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 • Q10 •
Question 02 (b)
For what value of the constant is the function continuous everywhere?
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When do we have ?
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The domain of the function is , because any polynomials are defined on the real line and the rational function is defined on . However, the domain of the function is because in order to compute , we have to use the branch as this one is defined for . (so )
On the domain, observe that for any value of , the function will be continuous for all and for all , so the only point to check is . The function will be continuous at if and only if
which by definition is equivalent to
and so will be continuous at if and only if . After solving for , we conclude that is continuous everywhere if and only if .
Answer: The function is continuous everywhere if and only if .
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