$\lim _ { x \rightarrow \infty } \frac { \sqrt { 9 x ^ { 4 } + 1 } } { x ^ { 2 } - 3 x + 5 }$ is
(A) 1
(B) 3
(C) 9
(D) nonexistent

Find the value of $\lim _ { x \rightarrow 0 } \frac { x ( x + 7 ) } { x }$. [3 points]

What is the value of $\lim _ { x \rightarrow - 2 } \frac { ( x + 2 ) \left( x ^ { 2 } + 5 \right) } { x + 2 }$? [2 points]
(1) 7
(2) 8
(3) 9
(4) 10
(5) 11

What is the value of $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 8 } { x - 2 }$? [2 points]
(1) 2
(2) 4
(3) 6
(4) 8
(5) 10

What is the value of $\lim _ { x \rightarrow \infty } \frac { \sqrt { x ^ { 2 } - 2 } + 3 x } { x + 5 }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

$\lim _ { x \rightarrow 3 } \frac { \sqrt { 3 x } - 3 } { \sqrt { 2 x - 4 } - \sqrt { 2 } }$ is equal to
(1) $\frac { 1 } { \sqrt { 2 } }$
(2) $\frac { 1 } { 2 \sqrt { 2 } }$
(3) $\frac { \sqrt { 3 } } { 2 }$
(4) $\sqrt { 3 }$

For each $t \in R$, let $[ t ]$ be the greatest integer less than or equal to $t$. Then $\lim _ { x \rightarrow 0 ^ { + } } x \left( \left[ \frac { 1 } { x } \right] + \left[ \frac { 2 } { x } \right] + \ldots + \left[ \frac { 15 } { x } \right] \right)$
(1) does not exist (in $R$ )
(2) is equal to 0
(3) is equal to 15
(4) is equal to 120

Let $[ t ]$ denote the greatest integer $\leq t$. If $\lambda \varepsilon R - \{ 0,1 \} , \quad \lim _ { x \rightarrow 0 } \left| \frac { 1 - x + | x | } { \lambda - x + [ x ] } \right| = L$, then $L$ is equal to
(1) 1
(2) 2
(3) $\frac { 1 } { 2 }$
(4) 0

$\lim _ { n \rightarrow \infty } \left( 1 + \frac { 1 + \frac { 1 } { 2 } + \ldots\ldots + \frac { 1 } { n } } { n ^ { 2 } } \right) ^ { n }$ is equal to
(1) $\frac { 1 } { e }$
(2) 0
(3) $\frac { 1 } { 2 }$
(4) 1

If $\lim _ { x \rightarrow \infty } \left( \sqrt { x ^ { 2 } - x + 1 } - a x \right) = b$, then the ordered pair $( a , b )$ is: (1) $\left( 1 , - \frac { 1 } { 2 } \right)$ (2) $\left( - 1 , \frac { 1 } { 2 } \right)$ (3) $\left( - 1 , - \frac { 1 } { 2 } \right)$ (4) $\left( 1 , \frac { 1 } { 2 } \right)$

The set of values of $a$ for which $\lim _ { x \rightarrow a } ( [ x - 5 ] - [ 2 x + 2 ] ) = 0$, where $[ \zeta ]$ denotes the greatest integer less than or equal to $\zeta$ is equal to
(1) $( - 7.5 , - 6.5 )$
(2) $( - 7.5 , - 6.5 ]$
(3) $[ - 7.5 , - 6.5 ]$
(4) $[ - 7.5 , - 6.5 )$

Let $f : \mathbb{R} \rightarrow (0, \infty)$ be strictly increasing function such that $\lim_{x \rightarrow \infty} \dfrac{f(7x)}{f(x)} = 1$. Then, the value of $\lim_{x \rightarrow \infty} \left(\dfrac{f(5x)}{f(x)} - 1\right)$ is equal to
(1) 4
(2) 0
(3) $\dfrac{7}{5}$
(4) 1

Some digits in the 11-digit phone numbers of Ayla and Berk are given as follows. $$\begin{aligned} & \text{Ayla} \longrightarrow 05{*}{*}{*}{*}{*}7235 \\ & \text{Berk} \longrightarrow 05{*}{*}{*}{*}{*}9415 \end{aligned}$$ Let $A$ be the set of digits in Ayla's phone number and $B$ be the set of digits in Berk's phone number, where $$\begin{aligned} & s(A) = 9 \\ & s(B) = 6 \end{aligned}$$ It is known that $A \cap B = \{0, 1, 4, 5, 6\}$. What is the sum of the values of elements in the set $A \setminus B$?
A) 18
B) 20
C) 21
D) 26
E) 27