Deneme Sınavı Soruları

Consider the following ODE subject to an initial condition

subject to an initial condition y(5)=1000, C=?

A type of toy is supplied according to the rule

and

units of this toy are sold at a price of 79 TL. What is the produces surplus?

What is the area under the graph of 

on the interval

A radioactive isotope has a half-life of 15 days. How much amount of isotope should we start with if we want to have 55 g isotope at the end of 60 days?

Solve the following ODE (ordinary differential equation)

Obtain the solution

explicitly from the initial value problem

Evaluate the integral

Evaluate the integral

What is the solution of the initial value problem

What is the indefinite integral of

I. The integration by parts method is derived from the differentiation rule of the product of any two functions.

II. In the method of integration by parts, first we need to choose u and v.  Then, we find du and dv and then we write all of these results.

III. Once we have taken the last integral in the problem, we will add in the constant of integration c to get our final answer.

What can be said to be true about integration by parts?

A country’s distribution of income is defined by the curve

What is the Gini index of this country?

Distribution of income of a country is given by the Lorenz curve

What is the Gini index of this country?

I. 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).

II. The family of all antiderivatives of a function f, F(x)+ c is called the indefinite integral of f.

III. The process of finding antiderivatives of a given function is called derivation.

What can be said to be true about indefinite integrals?

I. In the substitution method we change the variable of the integrand to something more convenient, or to put it more correctly, to a form where the previous rules may be applied directly.

II. This method is usually applied if a certain part of the integrand can be viewed as the derivative of remaining part of the integrand.

III. After integrating with respect to the new variable, it is not necessary to “back substitute” and getting the integral back in terms of the original variable.

What can be said to be true about the Change of Variable Method (Substitution Method)?

The Lorenz curve for the distribution of income in a certain country is defined by

What is the Gini index of this country?

What is the solution of the differential equation

The supply curve of a certain product is given by

What is the producer surplus when 40 units of this product are sold?

A certain item is supplied according to the rule S(q)=and its prices for an amount of units is 130 tl. What is the expected income?