turkey-yks 2013 Q37

turkey-yks · Other · lys1-math Small angle approximation

Let m, n be non-zero real numbers. The function
$$f ( x ) = \frac { x } { n } \sin \left( \frac { m } { x } \right)$$
has a horizontal asymptote at $y = 2$. Given this, which of the following is the relationship between m and n?
A) $m = n$
B) $m = n + 2$
C) $m = 2 n$
D) $m = 3 n$
E) $2 m = 3 n$

Let m, n be non-zero real numbers. The function

$$f ( x ) = \frac { x } { n } \sin \left( \frac { m } { x } \right)$$

has a horizontal asymptote at $y = 2$.\\
Given this, which of the following is the relationship between m and n?\\
A) $m = n$\\
B) $m = n + 2$\\
C) $m = 2 n$\\
D) $m = 3 n$\\
E) $2 m = 3 n$

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