Module 2. Analitic geometry. Introduction to Calculus
Individual Home Task
Variant 7
1. For the triangle with the vertices А(–10;5), В(14;–2), С(–4;2) 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;–1;1), M2(2;–1;–3), of the plane Р1: x–4y+3z–1=0, Р2: 3x–y–5z–8=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:
.
Module 2. Analitic geometry. Introduction to Calculus
Individual Home Task
Variant 8
1. For the triangle with the vertices А(0;7), В(6;–1), С(2;1) 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 М1(4;0;–2),
M2(3;4;–5),
of the plane Р1:
8x+2y–z+12=0,
Р2:
2x+y–z+2=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:
.