Mathematics 2

Yanıt Açıklaması: We consider the subintervals to evaluate L 4 (f) . By definition we obtain

Yanıt Açıklaması: For we have Hence, the area can be calculated with the formula Hence the right answer is D.

Yanıt Açıklaması: Starting with the trial solution We obtain Hence the general solution is The initial conditions gives us and by this equations we have Thus the solution of IVP is

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Yanıt Açıklaması: For an integrable function f on the definite integral can be written as Considering this we can write the question as So; So the correct answer is A.

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

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Yanıt Açıklaması: A function F is called an antiderivative of f on an interval (a, b) if F' (x) = f (x) for all x in (a, b). Thus, an antiderivative of is a function such that its derivative is We can take since

Yanıt Açıklaması: By the linearity of the definite integral it is clear that Hence the right answer is D.

Yanıt Açıklaması: Since this equation is an first order ODE with a constant coefficient, it is clear that y=ce 4x is the general solution.

Yanıt Açıklaması: We know the initial population P0=10000, and that at t=5 the population is P=10000∙1.10. Hence, from (13) herefore, after 20 years,

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

Yanıt Açıklaması: Correct answer is E .

Yanıt Açıklaması: Let us use the change of variables method. Let u=x 2 +3x+7 which gives du=(2x+3)dx and 2du=(4x+6)dx. Substituting these values into the integral we get where c is an arbitrary real number.

Yanıt Açıklaması: The sought for area is expressed in terms of the definite integral as