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# Math test with answers Part 2

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**04.07.2013**

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# Description

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;

# Additional information

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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