$$\lim _ { x \rightarrow \infty } \left( \sqrt { x ^ { 2 } + 2 x + 1 } - \sqrt { x ^ { 2 } + 1 } \right)$$
What is the value of this limit?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 5 } { 2 }$
D) 1
E) 2

$\lim _ { x \rightarrow \pi } \frac { x ^ { 2 } \cdot \sin ( \pi - x ) + \pi ^ { 2 } \cdot \sin ( x - \pi ) } { ( x - \pi ) ^ { 2 } }$\ What is the value of this limit?\ A) $- 2 \pi$\ B) $- \pi$\ C) $\pi$\ D) $2 \pi$\ E) $3 \pi$

A function f is defined on a subset of the set of real numbers as
$$f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x - 2 } + \frac { x ^ { 2 } - 6 x + 9 } { 2 x - 6 }$$
Accordingly, $$\lim _ { x \rightarrow 2 } f ( x ) + \lim _ { x \rightarrow 3 } f ( x )$$
what is the value of this expression?
A) $\frac { 3 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 4 }$
E) $\frac { 1 } { 4 }$

$$\lim_{x \rightarrow 1} \frac{(1 - \sqrt{x}) \cdot (\sqrt[3]{x} - 2)}{-x^{2} + 9x - 8}$$
What is the value of this limit?
A) 1 B) $\dfrac{1}{2}$ C) $\dfrac{1}{7}$ D) $\dfrac{1}{14}$ E) $\dfrac{1}{18}$