Chapter 1.1, Problem 50E

(a)

To determine

To calculate: Estimate the limits

Answer to Problem 50E

The limit is 1.

Explanation of Solution

Given information: The limit $\underset{h\to 2^{-}}{\lim }G(x)$

Calculation:

Trace the graph will reveal that it approaches the point $(2,1)$ since $x=2$ from the left, meaning that the limit is 1.

Therefore the required limit is 1.

(b)

To determine

To calculate: Estimate the limits

Answer to Problem 50E

The limit is 1.

Explanation of Solution

Given information: The limit is $\underset{h\to 2^{+}}{\lim }G(x)$

Calculation:

Trace the graph will reveal that it approaches the point $(2,1)$ since $x=2$ from the right, meaning that the limit is 1.

Therefore the required limit is 1.

(c)

To determine

To calculate: Estimate the limits

Answer to Problem 50E

The limit is 1.

Explanation of Solution

Given information: The limit is $\underset{h\to 2}{\lim }G(x)$

Calculation:

From 50a and 50b:

  $\begin{array}{c}\underset{x\to 2^{-}}{\lim }G(x)=\underset{x\to 2^{+}}{\lim }G(x)\\ =1\end{array}$

Hence the limit as $x$ approaches 2 exists and is 1.

Therefore the required limit is 1.

(d)

To determine

To calculate: Estimate the limits

Answer to Problem 50E

The limit is 3.

Explanation of Solution

Given information: The limit is $G(2)$

Calculation:

The closed point at 3 on the graph indicates that the value of the function $G(x)$ at 2 is equal to 3.

  $G(2)=3$

Therefore the required limit is 3.