Home > APCALC > Chapter 3 > Lesson 3.1.2 > Problem3-31

3-31.

Evaluate the following limits.

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

Think about the graph of $y = 3x^2$. Unlike most one-sided limits, this function approaches the same value from the left as it does from the right. You simply need to evaluate.

$3\cdot(4)^2 = 48$

1. $\lim\limits _ { x \rightarrow 3 ^ { + } } ( 6 - 2 x )$

Refer to the hint in part (a).

$\lim\limits _ { x \rightarrow 3 ^ { + } } ( 6 - 2 x )$

1. $\lim\limits _ { x \rightarrow \infty } ( \sqrt { x } )$

Think about the graph $y = \sqrt x$. What happens as $x\rightarrow \infty$? Is there a horizontal asymptote? If so, the $\lim\limits_{x\rightarrow \infty }$ will equal a constant. Or does the function keep increasing? If so, the $\lim\limits_{x\rightarrow \infty }$ will approach $\infty$. Think about the graph of $y=\sqrt{x}$. What happens as $x\rightarrow \infty ?$

1. $\lim\limits _ { x \rightarrow \infty } ( \frac { 1 } { x ^ { 2 } } )$

Refer to the hint in part (c). Note: you should be able to visualize the graph of$y=\frac{1}{x^{2}}$.