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Module 2. Analitic geometry. Introduction to Calculus

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Individual Home Task

Variant 5

1. For the triangle with the vertices А (–7;3), В (2;–1), С (–1;–5) find:

a) length of the side АВ;

b) equation of the line АМ which parallel to the side ВС;

c) the equation of the hieght ВF;

d) the equation of the median AD;

e) the interior angle ;

f) the coordinates of the points N and K, which divides the greater sige of the triangular into three equal parts;

g) area of the treangular АВС.

2. There are given the points М 1(1;–2;1), M 2(2;3;4), of the plane Р 1: x–2y+3z–4=0,
Р 2: 2x+3y–4z+5=0 and лінії L 1: ; L 2: .

а) Write down the equation of the straight line passing through the points М 1 and M 2;

b) Find the acute angle between the lines L 1 and L 2;

c) Through the point M 2 draw the plane parallel to the plane Р 2;

d) Find the acute angle between the planes Р 1 and Р 2;

e) Find the distance from the point М 1 to the plane Р 2;

f) Through the point M 2 draw the line parallel to the line L 2;

g) Find the acute angle between the line L 2 and the plane Р 2;

h) Through the point М 1 draw the line perpendicular to the plane Р 1;

i) Write down the equation of the plane passing through the point М 1 and perpendicular to the planes Р 1 and Р 2;

j) Write down the canonic equation of the line which is the concurent of two planes Р 1 and Р 2.

3. Calculate the limits: а) ; b) ;

c) ; d) .

4. Calculate the limits: а) ; b) .

5. Investigate the function for continuity:


Module 2. Analitic geometry. Introduction to Calculus

Individual Home Task

Variant 6

1. For the triangle with the vertices А (–8;–2), В (2;10), С (4;4) find:

a) length of the side АВ;

b) equation of the line АМ which parallel to the side ВС;

c) the equation of the hieght ВF;

d) the equation of the median AD;

e) the interior angle ;

f) the coordinates of the points N and K, which divides the greater sige of the triangular into three equal parts;

g) area of the treangular АВС.

2. There are given the points М 1(1;2;–6), M 2(–3;3;4), of the plane Р 1: x+y–z+4=0,
Р 2: 2x-y+4z+5=0 and лінії L 1: ; L 2: .

a) Write down the equation of the straight line passing through the points М 1 and M 2;

b) Find the acute angle between the lines L 1 and L 2;

c) Through the point M 2 draw the plane parallel to the plane Р 2;

d) Find the acute angle between the planes Р 1 and Р 2;

e) Find the distance from the point М 1 to the plane Р 2;

f) Through the point M 2 draw the line parallel to the line L 2;

g) Find the acute angle between the line L 2 and the plane Р 2;

h) Through the point М 1 draw the line perpendicular to the plane Р 1;

i) Write down the equation of the plane passing through the point М 1 and perpendicular to the planes Р 1 and Р 2;

j) Write down the canonic equation of the line which is the concurent of two planes Р 1 and Р 2.

3. Calculate the limits: а) ; b) ;

c) ; d) .

4. Calculate the limits: а) ; b) .

5. Investigate the function for continuity: .


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