csat-suneung 2005 Q28

csat-suneung · South-Korea · csat__math-humanities 4 marks Chain Rule Geometric Limit with Parametric Chain Rule

For two points $\mathrm { P } ( n , f ( n ) )$ and $\mathrm { Q } ( n + 1 , f ( n + 1 ) )$ on the graph of the quadratic function $f ( x ) = 3 x ^ { 2 }$, let $a _ { n }$ be the distance between them. Find the value of $\lim _ { n \rightarrow \infty } \frac { a _ { n } } { n }$. (Here, $n$ is a natural number.) [4 points]
(1) 9
(2) 8
(3) 7
(4) 6
(5) 5

For two points $\mathrm { P } ( n , f ( n ) )$ and $\mathrm { Q } ( n + 1 , f ( n + 1 ) )$ on the graph of the quadratic function $f ( x ) = 3 x ^ { 2 }$, let $a _ { n }$ be the distance between them. Find the value of $\lim _ { n \rightarrow \infty } \frac { a _ { n } } { n }$. (Here, $n$ is a natural number.) [4 points]\\
(1) 9\\
(2) 8\\
(3) 7\\
(4) 6\\
(5) 5

Paper Questions

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