Mathematics 2

Yanıt Açıklaması: Let us consider the trial solution we can substitute these functions into the equation: So the general solution is

Yanıt Açıklaması: The total revenue function can be found by integrating the marginal revenue function, thus we have Now, we should calculate R(20)-R(10).

Yanıt Açıklaması: If we integrate the marginal revenue, we obtain the total revenue. So, Since the fixed cost 180TL, we find that c=180. If we denote the quantity to be sold to gain 36TL by q 0 then we arrive at the equality:

Yanıt Açıklaması: By using the property of definite integral, we  can write then we get Then the correct answer is B.

Yanıt Açıklaması: Therefore the correct answer is the E option.

Yanıt Açıklaması: Using the points 0, , 1, let us divide the interval into two subintervals , has a maximum value M i on the each subinterval. That is

Yanıt Açıklaması: the correct answer is A.

Yanıt Açıklaması: We first calculate the quantity when the price is 9TL. Using the supply function, we find which gives q = 2. Inserting the given values in the formula we obtain Hence the correct answer is D.

Yanıt Açıklaması: Let u=8x 2 +2 which means  du=16xdx. If we write the integral with respect to the new variable u we have

Yanıt Açıklaması: For , let A 1 denote the area of the triangle under the x-axis and above the graph. For let A 2 denote the area of the triangle.

Yanıt Açıklaması: If we make a change of variables as we get, Returning back to the original variable x, we find that the antiderivative of f is . Thus, the definite integral is Therefore the correct answer is the D option.

Yanıt Açıklaması: The consumer surplus is evaluated taking into account the demand function. Since the equilibrium point is and we have Then the answer is C.

Yanıt Açıklaması: Let us calculate the Gini index for the first function. Inserting the Lorenz function into the formula for the Gini index given above, we obtain

Yanıt Açıklaması: This integral can be calculated by change of variables. Let then we get Returning back to the original variable x, we find that the antiderivative of Thus the definite integral is The correct answer is D.

Yanıt Açıklaması: To solve this problem, we should use If we say We know that Cancelling the factor and taking the logarithms of both sides is found as Hence, we have, Lastly, to find we will use Thus, The correct answer is A.

Yanıt Açıklaması: According to the statement of the problem we wish to have a mass of 20g after 32 days, i.e. at t=32 M=20

Yanıt Açıklaması: The Gini index is calculated using the formula where L(x) is the Lorenz curve. Inserting L(x) given in the question we find Hence the correct answer D.

Yanıt Açıklaması: Firstly, we need to determine the total cost function. This is achieved by integration as Now, the cost of building 2 units is When the production increases to 4 units we get To find the increase of the cost, we calculate the difference which gives