Mathematics 2

Yanıt Açıklaması: f (t) = 2000. The interest rate tells us that r = 0,2 and the time period is T = 4 years, so that the future value of the money is

Yanıt Açıklaması: By the Fundamental Theorem of Calculus we obtain The right answer is E.

Yanıt Açıklaması: Correct answer is A.

Yanıt Açıklaması: The price may be found as Correct answer is D

Yanıt Açıklaması: The original integral becomes

Yanıt Açıklaması: The two curves intersect each other at the points x=-1, x=1 since x 2 =2-x 2 => x=-1, x=1. That is, the region is on the interval [-1,1]. Thus, the required area is

Yanıt Açıklaması: We start from the trial solution Substituting these results in the ODE gives So, the general solution is given by The correct answer is D.

Yanıt Açıklaması: We first need to determine the intersection points of the given curves. To do so, let us equate them: The points satisfying the last equation are -2, 0, 2. Since there is an extra condition of x≥0, the points of intersection are 0 and 2. Also, in the interval 0≤x≤2, we have and therefore the required area A is evaluated as Therefore the correct answer is the C option.

Yanıt Açıklaması: We can find the total cost function C(x) by integrating the marginal cost function with respect to x.

Yanıt Açıklaması: The required area is We need to find the antiderivative F such that One of these functions satisfying If we invoke the Fundamental Theorem of Calculus

Yanıt Açıklaması: By the formula we have that means the right answer is E.

Yanıt Açıklaması: The price can be found as Using the integral formula for the producer surplus, we obtain:

Yanıt Açıklaması: The total revenue function can be found by integrating the marginal revenue. Therefore, We need to calculate The correct answer is B.

Yanıt Açıklaması: the correct answer is A.

Yanıt Açıklaması: Let Turning back to original variable , one of the antiderivative of the function Therefore the definite integral

Yanıt Açıklaması: If we write p 0 =5 in the demand function, we get that Since the demand quantity cannot be negative, x=6. Thus, the consumer surplus can be found as: