### Home > APCALC > Chapter 7 > Lesson 7.3.2 > Problem7-120

7-120.

Without a calculator, determine the following limits.

1. $\lim\limits _ { x \rightarrow \infty } ( 4 x + 2 - \frac { 3 } { x - 2 } )$

If you took the limit of each term separately, would any of those limits $= 0$?

1. $\lim\limits _ { x \rightarrow - \infty } \frac { 2 x ^ { 2 } + x - 21 } { 2 x ^ { 2 } + 5 x - 7 }$

Check the end behavior of the graph by comparing the highest powers from both the numerator and the denominator.

$\lim\limits_{x\rightarrow -\infty }\frac{2x^{2}}{2x^{2}}=\lim\limits_{x\rightarrow -\infty }1=\text{ _______ }$

1. $\lim\limits _ { x \rightarrow 0 + } ( \operatorname { ln } ( x ) + 18 )$

$\lim\limits_{x\rightarrow 0^{+}}\ln(x)+\lim\limits_{x\rightarrow 0^{+}}18=\text{ _____}$

1. $\lim\limits _ { x \rightarrow \frac { \pi } { 3 } } \frac { \operatorname { sin } ( x ) - \frac { \sqrt { 3 } } { 2 } } { x - \frac { \pi } { 3 } }$

This is Ana's Definition of the Derivative;
Find $f '\left(a\right)$

$f'(a)=\lim\limits_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$