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Math test, the number of jobs - 90.


Task 1


Question 1. What is called a function?


number;

a rule by which each value of argument x corresponds to one and only one value of y;

vector;

matrix;

there is no right answer.


Question 2. How is it possible to determine the inverse function?


where each element has a unique inverse image;

When the function is constant;

when the function is not defined;

When the function is multi-valued;

there is no right answer.


Question 3. What function is called Limited?


reverse;

the function f (x) is bounded, if mf (x) M;

complex;

the function f (x) is called bounded if f (x)> 0;

the function f (x) is called bounded if f (x) 0;


Question 4: What is the point is called a limit point of A?


null;

t.h0 called a limit point of A if every neighborhood of x0 contains a point of A different from x0;

not belonging to the set A;

there is no right answer;

lying on the boundary of the set.


Item 5. Can be a limit at the point when one-sided limits not equal?


Yes;

sometimes;

No;

always;

there is no right answer.




Task 2


Question 1. Is the function of infinitesimal when?


Yes;

No;

sometimes;

always;

there is no right answer.


Question 2. Is the function is infinitely large at?


Yes;

No;

sometimes;

if x = 0;

there is no right answer.


Question 3. Is the function y = sin x infinitely large when?


Yes;

No;

sometimes;

always;

there is no right answer.


Question 4. Is the function y = cos x infinitely large when?


Yes;

No;

sometimes;

always;

there is no right answer.


Question 5. Is the function y = tg x infinite in Vol. X0 = 0?


Yes;

sometimes;

always;

No;

there is no right answer.




Activity 3


Question 1. Is the product of an infinitesimal function on a limited function, infinitesimal function?


No;

Yes;

sometimes;

not always;

there is no right answer.


Question 2: When is infinitesimal  (x) and  (x) are called infinitesimal of the same order at x0?


if they are equal;

if;

if;

if the limits are 0;

there is no right answer.


Question 3. How many kinds of basic elementary functions we learned?


5;

1;

0;

2;

3.


Question 4: What is the limit of the constants?


0;

e;

1;

;

p.


Question 5. Is the power function continuous?


No;

Yes;

sometimes;

for x> 1;

there is no right answer.




Task 4


Question 1. Give the formula of the first remarkable limit.


;

uґ = kx + B;

there is no right answer.


Question 2. Give the formula of the second remarkable limit.


0;


Question 3: What functions are called continuous?


infinitesimal;

satisfying the following conditions: a) f is definable in t. in x0) exists and is equal to f (x0);

infinitely large;

degree;

trigonometric.


Question 4. If f (x0 + 0) = f (x0-0) = L, but f (x0) L, which is a function of the gap?


there is no right answer;

2nd kind;

Disposable;

ineradicable;

the function is continuous.


Question 5. What is the gap f (x) in t. X0 if f (x0-0) f (x0 + 0), and it is not known: Of course these limits?


Disposable;

ineradicable;

the function is continuous;

1st kind;

2nd kind.


Task 5


Question 1. Formulate the continuity of complex functions.


always difficult function is continuous;

If the function u = g (x) is continuous at x0 and the function y = f (u) is continuous at u = g (x0), then the composite function y = f (g (x)) is continuous at x0.

complex function is a composite of continuous functions is not continuous;

complex function is discontinuous;
Question 3. What is the derivative of the function?


The limit values \u200b\u200bof this function;

0;

1;

e


Question 4. What function is differentiable at x = 4?


ln (x-4);

having a derivative at x = 4;

is continuous at x = 4;

there is no right answer


Question 5. What function is called differentiable on (a, b)?


discontinuous at each interval;

differentiable at each point of the interval;

constant;

increasing;

decreasing.




Task 6


Question 1. What is the derivative of y = a constant?


1;

0;

e;

;

there is no right answer.


Question 2. What is the derivative of the function y = x5?


0;

1;

e;

5x4;

there is no right answer.


Question 3. What is the derivative of y = ex?


0;

ex;

e;

1;

there is no right answer.


Question 4: What is the derivative of y = ln x?


;

0;

e;

1;

there is no right answer.


Question 5. What is the derivative of y = sin x?


0;

cos x;

e;

1;

there is no right answer.




Task 7


Question 1. Can a continuous function be differentiable?


No;

Yes;

only at x =;

only at x = 0;

there is no right answer.


Question 2: Is it always a continuous function is differentiable?


always;

never;

not always;

at x = 0;

in Vol. x =.


Question 3: Can a differentiable function to be continuous?


No;

Yes;

never;

in Vol. x = 0;

in Vol. x =.


Question 4. Is it always a differentiable function is continuous?


not always;

never;

there is no right answer;

in Vol. x = 0;

always.


Question 5. Find the second derivative of the function y = sin x.


cos x;

-sin x;

0;

1;

tg x.




Task 8


Question 1. What is the main linear part of the increment function?


derivative;

Differential (DN);

function;

infinitesimal;

infinitely large.


Question 2. State the L'Hospital's rule.


If the right-hand side there is a limit;

;

;

there is no right answer;


Question 3: Which types of uncertainties can be opened using L'Hospital's rule?


{0};

;

cx 0;

cx;

x.


Question 4. Is the condition of the y = 0 at the point, which is not a boundary point of the domain of a differentiable function at the necessary condition for the existence of extremum at this point?


No;

Yes;

not always;

sometimes;

there is no right answer.


Question 5. Is the condition of the j = 0 m. X = a sufficient condition for the existence of extrema?


Yes;

No;

not always;

sometimes;

there is no right answer.




Task 9


Question 1. What function is called a function of two variables?


f (x);

n = f (x, y, z);

there is no right answer;

z = f (x, y);

f (x) = const = c.


Question 2. Calculate the limit of the function.


0;

29;

1;

5;

2.


Question 3: Calculate the limit of


0;

1;

16;

18;

20.


Q4: Which lines are called lines of discontinuity?


straight;

consisting of break points;

parabola;

ellipses;

there is no right answer.


Question 5. Find the first derivative of the function at z = 3x + 2y.


1;

2;

0;

5;

there is no right answer.




Task 10


Question 1. What is the function whose derivative is the given function?

Question 2. Locate the erroneous expression if - one of the primitives for a function, and C - arbitrary constant.

etc.


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27.12.2017 1:37:00
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24.06.2016 18:53:03
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