Mathematics 2

Yanıt Açıklaması: Let us put and substitute it into the differential equation. Then the characteristic equation is So, the general equation can be written as The correct answer is E.

Yanıt Açıklaması: the correct answer is A.

Yanıt Açıklaması: Substituting into suggested equations, we find that the only equation that is satisfied is D) indeed Correct answer is  D .

Yanıt Açıklaması: h(2)=2 . 2 2 +2a-1=7+2a. Since h(2)=15, then 7+2a=15. If we solve this equation 2a=8. And we obtain a=4.

Yanıt Açıklaması: The area under the graph of the supply function corresponds to the expected income, so

Yanıt Açıklaması:

Yanıt Açıklaması: As before   we only need to apply the formula for the future value of income . Since the time period is and the interest rate gives we have Correct answer is A

Yanıt Açıklaması: Let u=x 3 +4 then du=3x 2 dx. Thus we obtain

Yanıt Açıklaması: In a certain market, if a producer who is willing to sell a product at a certain price may sell the product higher than the price he asks, then he has increased his revenue. This extra amount gained is called the producer surplus (PS). In other words, the producer surplus is the difference of the price the producer is willing to sell and the actual price he sells his product.

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Yanıt Açıklaması: Since given parabola intersects at and the required area is under the then we evaluate required area by the definite integral below: Thus, the right answer is D.

Yanıt Açıklaması: Let us use the integration by parts method. Let u=4x+10 which gives du=4dx. Also, let dv=e 2x dx which gives . Substituting these values into ∫udv=uv-∫vdu  we get; for any arbitrary real number c.

Yanıt Açıklaması: on the interval [-2, 1], therefore the sought for area A can be calculated by definite integral: The antiderivative of is so Therefore the correct answer is the C option.

Yanıt Açıklaması: First, we must find q 0 : Since the area under the graph of the supply function corresponds to the expected income, we can evaluate it by integrating the supply function from q = 0 to q = 3 which gives

Yanıt Açıklaması: Substituting in the equation we get Hence so the general solution of the  equation is

Yanıt Açıklaması:

Yanıt Açıklaması: The solution is quite straightforward. Using the integral formula for Gini index, we get