turkey-yks 2012 Q40

turkey-yks · Other · lys1-math Applied differentiation Limit evaluation involving derivatives or asymptotic analysis

For a function f defined on the set of real numbers
$$\begin{aligned} & \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = 1 \\ & \lim _ { x \rightarrow 3 ^ { - } } f ( x ) = 2 \end{aligned}$$
Given this, what is the value of the limit $\lim _ { x \rightarrow 2 ^ { + } } \frac { f ( 2 x - 1 ) + f ( 5 - x ) } { f \left( x ^ { 2 } - 1 \right) }$?
A) $\frac { -1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) 1
D) 3
E) 4

For a function f defined on the set of real numbers

$$\begin{aligned}
& \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = 1 \\
& \lim _ { x \rightarrow 3 ^ { - } } f ( x ) = 2
\end{aligned}$$

Given this, what is the value of the limit $\lim _ { x \rightarrow 2 ^ { + } } \frac { f ( 2 x - 1 ) + f ( 5 - x ) } { f \left( x ^ { 2 } - 1 \right) }$?

A) $\frac { -1 } { 2 }$\\
B) $\frac { 3 } { 2 }$\\
C) 1\\
D) 3\\
E) 4

Paper Questions

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