Question 1

Let   Determine the following limit. (Hint: Use the graph to calculate the limit.)    &#10;A) 6&#10;B) 25&#10;C) 1&#10;D) 5&#10;E) does not exist.

Accepted Answer

Using the graph, we can see that as x approaches 2 from the left, the function approaches 5. And as x approaches 2 from the right, the function approaches 7. Therefore, the limit as x approaches 2 from both sides exists and is equal to 6.

Question 2

A ring has a inner circumference of 9 centimeters. If the ring's inner circumference can vary between 8 centimeters and 10 centimeters how can the radius vary? Round your answer to five decimal places.

A) Radius can vary between 6.48456 centimeters and 10.13212 centimeters.
B) Radius can vary between 1.59577 centimeters and 1.78412 centimeters.
C) Radius can vary between 1.27324 centimeters and 1.59155 centimeters.
D) Radius can vary between 2.54648 centimeters and 3.18310 centimeters.
E) Radius can vary between 0.43239 centimeter and 2.43239 centimeters.

Accepted Answer

The circumference of a circle is calculated using the formula:

C = 2πr

Where C is the circumference and r is the radius.

Given that the inner circumference of the ring is 9 centimeters, we have:

9 = 2πr

Solving for r, we get:

r = 9 / (2π)

r ≈ 1.43239 centimeters

Next, we need to find the range of values for r when the inner circumference varies between 8 and 10 centimeters.

When the inner circumference is 8 centimeters, we have:

8 = 2πr

r = 8 / (2π)

r ≈ 1.27324 centimeters

When the inner circumference is 10 centimeters, we have:

10 = 2πr

r = 10 / (2π)

r ≈ 1.59155 centimeters

Therefore, the radius can vary between 1.27324 centimeters and 1.59155 centimeters. Thus, the answer is C.

Question 3

Complete the table and use the result to estimate the limit.      &#10;A) 0.974745&#10;B) -1.099745&#10;C) -1.224745&#10;D) 1.058078&#10;E) 1.224745

Accepted Answer

-1.224745

Question 4

Complete the table and use the result to estimate the limit.      &#10;A)  &#10;B) 0&#10;C) 1&#10;D) 0.5&#10;E)

Accepted Answer

Based on the given table, as x approaches 0 from both sides, the values of f(x) approach 1. Therefore, by the definition of a limit, the limit of f(x) as x approaches 0 exists and is equal to 1.

Question 5

Complete the table and use the result to estimate the limit.      &#10;A) 0.525000&#10;B) 0.275000&#10;C) -0.100000&#10;D) 0.400000&#10;E) -0.475000

Accepted Answer

The answer of Complete the table and use the result...

Question 6

Determine the following limit. (Hint: Use the graph to calculate the limit.)    &#10;A) 6&#10;B) 1&#10;C) 5&#10;D) 4&#10;E) does not exist

Accepted Answer

The answer of Determine the following limit. (Hint: Use the...

Question 7

A sphere has a volume of 4.76 cubic inches. What is the radius of the sphere? Round your answer to four decimal places.&#10;A) 1.0435 inches&#10;B) 1.6565 inches&#10;C) 1.0660 inches&#10;D) 2.1320 inches&#10;E) 1.9335 inches

Accepted Answer

The volume of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$. To find the radius, we rearrange the formula to solve for $r$: $r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$. Substituting $V = 4.76$ cubic inches into the formula gives $r \approx 1.0435$ inches.

Question 8

Complete the table and use the result to estimate the limit.      &#10;A) -0.062500&#10;B) 0.067500&#10;C) -0.192500&#10;D) 0.047500&#10;E) -0.172500

Accepted Answer

The answer of Complete the table and use the result...

Question 9

A ring has a inner circumference of 10 centimeters. What is the radius of the ring? Round your answer to four decimal places.&#10;A) 0.7958 centimeter&#10;B) 3.1831 centimeters&#10;C) 1.5915 centimeters&#10;D) 1.7841 centimeters&#10;E) 10.1321 centimeters

Accepted Answer

The formula for circumference is C=2πr, where C is the circumference and r is the radius. 
We know the inner circumference of the ring is 10 centimeters, so we plug that in for C: 
10=2πr 
Divide both sides by 2π: 
r=10/2π 
Using a calculator and rounding to four decimal places, we get: 
r=1.5915 centimeters

Question 10

Determine the following limit. (Hint: Use the graph to calculate the limit.)    &#10;A) 5&#10;B) 1&#10;C) 0&#10;D) 4&#10;E) does not exist

Accepted Answer

The answer of Determine the following limit. (Hint: Use the...

Question 11

A sphere has a volume of 5.2 cubic inches. If the sphere's volume can vary between 4.4 cubic inches and 6.1 cubic inches , how can the radius vary? Round your answer to five decimal places.&#10;A) Radius can vary between 1.01653 inches and 1.13348 inches.&#10;B) Radius can vary between 1.61365 inches and 1.79929 inches.&#10;C) Radius can vary between 0.27474 inch and 1.97474 inches.&#10;D) Radius can vary between 1.85897 inches and 2.18882 inches.&#10;E) Radius can vary between 1.02490 inches and 1.20676 inches.