Mathematics 2

Yanıt Açıklaması: Using the points let us divide the interval into four subintervals and Since the function f is an increasing function, it takes its smallest values at the left end of each interval. The length of each subinterval is and therefore

Yanıt Açıklaması: the correct answer is C.

Yanıt Açıklaması: We need to calculate the future value of a continuous income stream, hence

Yanıt Açıklaması: We assume that and it then follows that m must be a root of the characteristic equation Thus the possible values of the general solution of the differential equation is

Yanıt Açıklaması: Since we clearly see that

Yanıt Açıklaması: the correct answer is E.

Yanıt Açıklaması: It is obvious that which means the right answer is C.

Yanıt Açıklaması: where c=c 1 +c 2 +c 3 .  After these calculations we obtain the integral as

Yanıt Açıklaması:

Yanıt Açıklaması: Using the initial condition hence “+” sign chosen The correct answer is B.

Yanıt Açıklaması: If then the characteristic equation is and its roots are Therefore the general solution of the differential equation is Applying the initial conditions, we obtain the following two equations for The solution of these equations is and the solution of the initial value problem is

Yanıt Açıklaması: The differential equation can be written as Integrating the left side with respect to and the right side with respect to gives

Yanıt Açıklaması: For this question, we only need to apply formula for the future value of an income. Since the time period T=3 and the interest rate r=0,2 is given, we have,

Yanıt Açıklaması: The average value is calculated using the definite integral as follows:

Yanıt Açıklaması: Consumer surplus is derived whenever the price a consumer actually pays is less than they are prepared to pay. A demand curve indicates what price consumers are prepared to pay for a hypothetical quantity of a good, based on their expectation of private benefit.

Yanıt Açıklaması: The total revenue function may be found by integrating the marginal revenue, so that we have

Yanıt Açıklaması: Let us use the change of variables method. Let  u=x 3 +6   which gives Substituting these values into the integral we get where c is an arbitrary real number.