csat-suneung 2009 Q6

csat-suneung · South-Korea · csat__math-science 3 marks Curve Sketching Finding Parameters for Continuity

For the function $f ( x ) = x ^ { 2 } - 4 x + a$ and the function $g ( x ) = \lim _ { n \rightarrow \infty } \frac { 2 | x - b | ^ { n } + 1 } { | x - b | ^ { n } + 1 }$, let $h ( x ) = f ( x ) g ( x )$. What is the value of $a + b$, the sum of the two constants $a , b$ such that the function $h ( x )$ is continuous for all real numbers $x$? [3 points]
(1) 3
(2) 4
(3) 5
(4) 6
(5) 7

For the function $f ( x ) = x ^ { 2 } - 4 x + a$ and the function $g ( x ) = \lim _ { n \rightarrow \infty } \frac { 2 | x - b | ^ { n } + 1 } { | x - b | ^ { n } + 1 }$, let $h ( x ) = f ( x ) g ( x )$. What is the value of $a + b$, the sum of the two constants $a , b$ such that the function $h ( x )$ is continuous for all real numbers $x$? [3 points]\\
(1) 3\\
(2) 4\\
(3) 5\\
(4) 6\\
(5) 7

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q26 Q26b Q27 Q27b Q28 Q28b Q29 Q29b Q30