Module 2. Analitic geometry. Introduction to Calculus
Individual Home Task
Variant 1
1. For the triangle with the vertices А(-3;5), В(11;-12), С(-7;12) 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(3;-1;2), M2(2;4;-2), planes Р1: 2x+3y-4z+5=0, Р2: x-y+z+2=0 and lines L1:
;
L2:
.
а) Write down the equation of the straight line passing through the points М1 і M2;
b) Find the acute angle between the lines L1 і L2;
c) Through the point M2 draw the plane parallel to the plane Р2;
d) Find the acute angle between the planes Р1 і 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 2
1. For the triangle with the vertices А(-3;4), В(-4;-3), С(8;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(3;1;–4),
M2(1;–3;2),
of the plane Р1:
2x
– y
– z
+
4=0,
Р2:
x-4y+5z-1=0
and
lines 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.