CPM Homework Help : CALC3RD Problem 7-132

Evaluate each limit.

$\lim\limits _ { x \rightarrow \infty } \frac { x } { \sqrt { x ^ { 2 } + 2 } }$
Hint (a):
Only consider the highest power in the numerator and the denominator. If they are the same, remember to account for their coefficients.

$\lim\limits _ { x \rightarrow - \infty } \frac { x } { \sqrt { x ^ { 2 } + 2 } }$
Hint (b):
For some limits, approaching $−∞$ will lead to a different result than approaching $+∞$ . This is one of those cases. Explain.

$\lim\limits _ { x \rightarrow 2 } \frac { \frac { 1 } { x } - \frac { 1 } { 2 } } { x ^ { 2 } - 4 }$
Hint (c):
Reduce the complex fraction to a more simplified version. Factor the denominator. Simplify. At this point, you should be able to substitute $2$ into the expression and not get division by $0$ .
Answer (c):
$-\frac{1}{16}$