Module 2. Analitic geometry. Introduction to Calculus
Individual Home Task
Variant 3
1. For the triangle with the vertices А(2;5), В (–6;-4), С (6;–3) 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.
There are given the points М1(1;–2;0), M2(2;–3;2), of the plane Р1: 2x+3y-4z-2=0,
Р2:
2x-y+z+9=0
and
lines лінії L1:
;
L2:
.
а) Write down the equation of the straight line passing through the points М1 and M2;
b) Find the acute angle between the lines L1 and L2;
c) Through the point M2 draw the plane parallel to the plane Р2;
d) Find the acute angle between the planes Р1 and Р2;
e) Find the distance from the point М1 to the plane Р2;
f) Through the point M2 draw the line parallel to the line L2;
g) Find the acute angle between the line L2 and the plane Р2;
h) Through the point М1 draw the line perpendicular to the plane Р1;
i) Write down the equation of the plane passing through the point М1 and perpendicular to the planes Р1 and Р2;
j) Write down the canonic equation of the line which is the concurent of two planes Р1 and Р2.
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 4
1. For the triangle with the vertices А(-5;-2), В(7;6), С(5;-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.
There are given the points М1(1;-2;-4), M2(2;–1;3), of the plane Р1: 5x+3y-4z+8=0, Р2: x-y+z+5=0 and лінії L1:
;
L2:
.
а) Write down the equation of the straight line passing through the points М1 and M2;
b) Find the acute angle between the lines L1 and L2;
c) Through the point M2 draw the plane parallel to the plane Р2;
d) Find the acute angle between the planes Р1 and Р2;
e) Find the distance from the point М1 to the plane Р2;
f) Through the point M2 draw the line parallel to the line L2;
g) Find the acute angle between the line L2 and the plane Р2;
h) Through the point М1 draw the line perpendicular to the plane Р1;
i) Write down the equation of the plane passing through the point М1 and perpendicular to the planes Р1 and Р2;
j) Write down the canonic equation of the line which is the concurent of two planes Р1 and Р2.
3.
Calculate the limits:
а)
;
b)
;
c)
;
d)
.
4.
Calculate the limits:
а)
;
b)
.
5.
Investigate the function for continuity: