turkey-yks 2011 Q38

turkey-yks · Other · lys1-math Small angle approximation
$$\lim _ { x \rightarrow \infty } \left( \sqrt { x ^ { 2 } + 2 x + 1 } - \sqrt { x ^ { 2 } + 1 } \right)$$
What is the value of this limit?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 5 } { 2 }$
D) 1
E) 2
$$\lim _ { x \rightarrow \infty } \left( \sqrt { x ^ { 2 } + 2 x + 1 } - \sqrt { x ^ { 2 } + 1 } \right)$$

What is the value of this limit?\\
A) $\frac { 1 } { 2 }$\\
B) $\frac { 3 } { 2 }$\\
C) $\frac { 5 } { 2 }$\\
D) 1\\
E) 2