Question 1

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges

Accepted Answer

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Question 2

Determine whether the improper integral   diverges or converges.&#10;A)  &#10;B)

Accepted Answer

The given improper integral is:

∫1^(∞) e^(-x²) dx

To determine whether it converges or diverges, we can use the integral test.

Let f(x) = e^(-x²).

Since f(x) is a positive, decreasing function for all x ≥ 1, we can use the integral test:

∫1^(∞) e^(-x²) dx converges if and only if the series ∑(n=1 to ∞) e^(-n²) converges.

This series is known as the Gaussian series or the error function, and it is well-known to converge. Therefore, the integral converges.

Since only option B indicates that the integral converges, the answer is B.

Question 3

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges

Accepted Answer

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Question 4

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)

Accepted Answer

We need to determine the convergence of the improper integral:

∫(from 1 to infinity) e^(x^2+1) / x^3 dx

We can use the Comparison Test to determine the convergence of this integral:

For x ≥ 1, we have e^(x^2+1) / x^3 ≥ e^(1+1) / x^3 = (e^2) / x^3

Now, consider the integral:

∫(from 1 to infinity) (e^2/x^3) dx

This is a p-series with p=3, and therefore it converges.

By the Comparison Test, our original integral also converges.

Therefore, the correct choice is B, and we cannot evaluate the integral because it does not have a closed-form solution.

Question 5

Suppose the capitalized cost C is given by where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

A) 681,400
B) 1,753,400
C) 1,799,511
D) 681,420
E)

<strong>Suppose the capitalized cost C is given by where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.</strong> A) 681,400 B) 1,753,400 C) 1,799,511 D) 681,420 E) <div style=padding-top: 35px>

Accepted Answer

The answer of Suppose the capitalized cost C is given...

Question 6

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C) diverges&#10;D)  &#10;E)

Accepted Answer

The answer of Determine whether the improper integral  ...

Question 7

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges

Accepted Answer

The answer of Determine whether the improper integral  ...

Question 8

Find the area between the x-axis and the graph of the function   .  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Find the area between the x-axis and...

Question 9

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges

Accepted Answer

The answer of Determine whether the improper integral  ...

Question 10

Determine whether the improper integral   diverges or converges.&#10;A) converges&#10;B) diverges

Accepted Answer

The integral is of the form ∫e^x/x^p dx, where p=1/2. This is known as an exponential integral, and it can be shown that it converges only for p>1. Since our p is less than 1, the integral diverges.

Question 11

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges

Accepted Answer

The answer of Determine whether the improper integral  ...

Question 12

Suppose the capitalized cost C is given by where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

A) 681,400
B) 1,753,400
C) 1,799,511
D) 681,420
E)

Accepted Answer

The answer of Suppose the capitalized cost C is given...

Question 13

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A) 18&#10;B) 9&#10;C)  &#10;D) 3&#10;E) diverges

Accepted Answer

The answer of Determine whether the improper integral  ...

Question 14

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) diverges