Chapter 1.1, Problem 46E

(a)

To determine

To calculate: Estimate the limits

Answer to Problem 46E

The limit is 5

Explanation of Solution

Given information: The limit is $\underset{x\to 4^{-}}{\lim }g(t)$

Calculation:

If trace the graph as move toward $t=-4$ from the left, see that the graph moves toward the point $(-4,5)$ hence the limit is 5.

Therefore the limit is 5.

(b)

To determine

To calculate: Estimate the limits

Answer to Problem 46E

The limit is 2.

Explanation of Solution

Given information: The limit is $\underset{x\to 4^{+}}{\lim }g(t)$

Calculation:

If trace the graph as move toward $t=-4$ from the left, see that the graph moves toward the point $(-4,2)$ hence the limit is 2.

Therefore the limit is 2.

(c)

To determine

To calculate: Estimate the limits

Answer to Problem 46E

The limit does not exists.

Explanation of Solution

Given information: The limit is $\underset{x\to 4}{\lim }g(t)$

Calculation:

As time approaches -4 from the left, the limit of $g(t)$ is 5. As t approaches -4 from the right, the limit of $g(t)$ is 2. The limit of $g(t)$ as t approaches -4 does not exist because these are not equivalent.

Therefore the limit does not exists.

(d)

To determine

To calculate: Estimate the limits

Answer to Problem 46E

The limit is 2.

Explanation of Solution

Given information: The function is $g(-4)$

Calculation:

The closed point at 2 when $t=4$ represents the value of $g(-4)$ as being equal to 2.

The required limit is 2.