csat-suneung 2014 Q18

csat-suneung · South-Korea · csat__math-B 4 marks Standard trigonometric equations Count zeros or intersection points involving trigonometric curves

For a natural number $n$, let $a _ { n }$ be the $n$-th smallest $x$-coordinate among the intersection points of the line $y = n$ and the graph of the function $y = \tan x$ in the first quadrant.
What is the value of $\lim _ { n \rightarrow \infty } \frac { a _ { n } } { n }$? [4 points]
(1) $\frac { \pi } { 4 }$
(2) $\frac { \pi } { 2 }$
(3) $\frac { 3 } { 4 } \pi$
(4) $\pi$
(5) $\frac { 5 } { 4 } \pi$

For a natural number $n$, let $a _ { n }$ be the $n$-th smallest $x$-coordinate among the intersection points of the line $y = n$ and the graph of the function $y = \tan x$ in the first quadrant.

What is the value of $\lim _ { n \rightarrow \infty } \frac { a _ { n } } { n }$? [4 points]\\
(1) $\frac { \pi } { 4 }$\\
(2) $\frac { \pi } { 2 }$\\
(3) $\frac { 3 } { 4 } \pi$\\
(4) $\pi$\\
(5) $\frac { 5 } { 4 } \pi$

Paper Questions

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