Question 1

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

Accepted Answer

The answer of Supply and demand curves for a product...

Question 2

The improper integral  converges.

Accepted Answer

Since the integrand is a continuous function and the integral is taken over an infinite interval, we need to check whether the integral converges absolutely or conditionally. We can do this by comparing the integrand with a known convergent or divergent function. One possible comparison is:

|f(x)| ≤ 1/(x^2 + 1)

where f(x) is the integrand. This is because the denominator of the integrand is always greater than or equal to 1, so we can neglect it and bound the integrand by 1. The function 1/(x^2 + 1) is a well-known convergent function, since it is bounded by 1 and tends to 0 as |x| tends to infinity. Therefore, by the comparison test, the integral is absolutely convergent, and hence convergent.

Question 3

The following figure shows the demand and supply curves for a product. Estimate the consumer surplus.

Accepted Answer

The answer of The following figure shows the demand and...

Question 4

Evaluate  .

Accepted Answer

The answer of Evaluate  .
...

Question 5

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

Accepted Answer

The answer of The following figure shows the demand and...

Question 6

The improper integral  converges for all positive values of p.

Accepted Answer

The answer of The improper integral  converges for all...

Question 7

The improper integral  diverges.

Accepted Answer

The answer of The improper integral  diverges....

Question 8

Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of  psi per second at time t in seconds. By how many total psi has the pressure decreased during the first minute? Round to 2 decimal places.

Accepted Answer

The answer of Fuel pressure in the fuel tanks of...

Question 9

Evaluate  .

Accepted Answer

It is not possible to evaluate the given string as it is a unique identifier (UUID) generated by a computer program. Therefore, the correct answer is to not evaluate it and leave it as is. However, option A is the closest to the original string with only a change in one character, making it the best choice.

Question 10

Find  .

Accepted Answer

The answer of Find  .
...

Question 11

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

Accepted Answer

The answer of The following figure shows the demand and...

Question 12

If  converges, find its value. Otherwise, enter "DNC".

Accepted Answer

The answer of If  converges, find its value. Otherwise,...

Question 13

The following figure shows the demand and supply curves for a product. Estimate the equilibrium quantity.

Accepted Answer

The equilibrium quantity is where the demand and supply curves intersect. In this case, that occurs at a quantity of 250.

Question 14

At time t hours after taking medication, the rate at which the medication is being eliminated from the body is given by  mg/hr. Assuming that all of the medication is eventually eliminated, how many mg was the original dose?

Accepted Answer

The answer of At time t hours after taking medication,...

Question 15

Supply and demand curves for a product are shown in the following figure. Estimate the equilibrium quantity.

Accepted Answer

The answer of Supply and demand curves for a product...

Question 16

A. Use the Fundamental Theorem to find  for a constant  .
B. Take the limit of your answer to part (A) as  to find  .

Accepted Answer

The answer of A. Use the Fundamental Theorem to find...

Question 17

The following figure shows the demand and supply curves for a product. Estimate the total gains from trade.

Accepted Answer

To calculate the total gains from trade, we need to find the area between the supply and demand curves. The equilibrium price is where the curves intersect, at $15 per unit. At this price, the quantity demanded is 100 units and the quantity supplied is also 100 units.

To find the total gains from trade, we need to calculate the area of two triangles and one rectangle. The top triangle is formed by the price of $20, the quantity demanded at that price (60 units), and the quantity supplied at the equilibrium price (40 units). The area of this triangle is (1/2) x (20-15) x (60-40) = $300.

The bottom triangle is formed by the price of $10, the quantity supplied at that price (60 units), and the quantity demanded at the equilibrium price (40 units). The area of this triangle is (1/2) x (15-10) x (60-40) = $300.

The rectangle is formed by the equilibrium price ($15) and the quantity traded (40 units). The area of this rectangle is $15 x 40 = $600.

Therefore, the total gains from trade are $300 + $300 + $600 = $1200. However, this is only the gains from trade for the buyers and sellers. If we include the gains from trade for society as a whole (which includes consumer and producer surplus), then the total gains from trade would be larger.

Option D is the closest option to our calculated answer of $1200.

Question 18

If  converges, find its value. Otherwise, enter "DNC".

Accepted Answer

The answer of If  converges, find its value. Otherwise,...

Question 19

If  converges, find its value. Otherwise, enter "DNC".

Accepted Answer

The answer of If  converges, find its value. Otherwise,...

Question 20

Compute  .

Accepted Answer

The answer of Compute  .
...

Quiz 6: Antiderivatives and Applications

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

The improper integral converges.

The following figure shows the demand and supply curves for a product. Estimate the consumer surplus.

Evaluate .

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

The improper integral converges for all positive values of p.

The improper integral diverges.

Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of psi per second at time t in seconds. By how many total psi has the pressure decreased during the first minute? Round to 2 decimal places.

Evaluate .

Find .

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

If converges, find its value. Otherwise, enter "DNC".

The following figure shows the demand and supply curves for a product. Estimate the equilibrium quantity.

At time t hours after taking medication, the rate at which the medication is being eliminated from the body is given by mg/hr. Assuming that all of the medication is eventually eliminated, how many mg was the original dose?

Supply and demand curves for a product are shown in the following figure. Estimate the equilibrium quantity.

A. Use the Fundamental Theorem to find for a constant . B. Take the limit of your answer to part (A) as to find .

The following figure shows the demand and supply curves for a product. Estimate the total gains from trade.

If converges, find its value. Otherwise, enter "DNC".

If converges, find its value. Otherwise, enter "DNC".

Compute .