### Home > APCALC > Chapter 7 > Lesson 7.3.3 > Problem7-132

7-132.

Evaluate each limit. Homework Help ✎

1. $\lim\limits _ { x \rightarrow \infty } \frac { x } { \sqrt { x ^ { 2 } + 2 } }$

Only consider the highest power in the numerator and the denominator. If they are the same, remember to account for their coefficients.

2. $\lim\limits _ { x \rightarrow - \infty } \frac { x } { \sqrt { x ^ { 2 } + 2 } }$

For some limits, approaching −∞ will lead to a different result than approaching +∞. This is one of those cases. Explain.

3. $\lim\limits _ { x \rightarrow 2 } \frac { \frac { 1 } { x } - \frac { 1 } { 2 } } { x ^ { 2 } - 4 }$

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.

$-\frac{1}{16}$