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MAT110U

MATHEMATICS II - Deneme Sınavı - 19

Ara Sınav 51850
Soru 1
Which of the following is the general solution of the ODE ?
Soru 2
What is the solution of the initial value problem , y(0)=2?
Soru 3
What is the solution of the differential equation ?
Soru 4
What is the solution of the initial value problem , y(0)=3/2?
Soru 5
Which of the following equations has the particular solution ?
Soru 6
What is the general solution of ?
Soru 7
What is the antiderivative of the indefinite integral  ∫ x2/4 dx?
Soru 8
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?

Soru 9
From the fundamental rules of integration which is the rule that states ?
Soru 10
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)?

Soru 11
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?

Soru 12
What is the equation used in the intagration by parts method?
Soru 13
What is the antiderivative of the integral ∫ 2.ex+4.dx value equal to?
Soru 14
I. ∫kdx = kx + c

II. ∫xrdx = xr -1/r - 1 + c

III. ∫1/x .dx = lnx +c , x>0

Which of the given basic rule can be said to be true?

Soru 15
What is the antiderivative of the integral ∫ 2.e2x + (2x2 - 4x + 1).dx value equal to?
Soru 16
I. The calculation of areas of planar regions bounded by given curves was achieved through a method called the method of exhaustion by inscribing and circumscribing the region in question by polygons the areas of which were either known or were easy to calculate.

II. Archimedes (B.C. 287-212) used this method to calculate the area of a circle (disk) by inscribing and circumscribing the circle with polygons. 

III. The area of a bounded region determined by the graph of the function y=f (x). We assume that the function f (x) is defined and continuous on a closed interval [a,b], and it is also negative, i.e. f (x) ≤ 0. 

What can be said to be true about area problems?

Soru 17
I. The definite integral of a function is a real number.

II. The numbers a and b are called the lower and upper limits of the integral.

III. The variable the integral is calculated, dx, is called the integrand

What can be said to be true about definite integrals?

Soru 18
What can be said to be true about the properties of the definite integrals?
Soru 19
I. The antiderivative F of the function f will be found, i.e. ∫ f(x)dx = F(x), then, to evaluate the definite integral, the difference F(b)–F(a) will be calculated.

II. The antiderivative F of the function f will be found, i.e. ∫ f(x)dx = F(x), then, to evaluate the definite integral, the difference F(b)+F(a) will be calculated.

III. Let f be a continuous function defined on the interval [a,b] and let there be an antiderivative function F defined on the interval [a,b] such that F ' (x)=f (x). 

What can be said to be true about the fundamental theorem of calculus?

Soru 20