Math Project

TERM HOMEWORK / NOV - DEC 2014

Name ……………………………….…………….

Student’s ID Number Constants a b c

1 Find the inverse 1X  if the matrix X is given by the equation:

1 0 3 2 1

. 2 1 4 2 3 .

2 3 1 3 4

а c

X b

c

        

             

2 Calculate 2 ?D L  if given two determinants:

1 3 0 1 2

2 2 0 2 3 .

0 4 5 3 4

0 5 2 1

b а c

a b D and L b

b c c

c

  

   

  

 

3 Given the triangle АBC with its vertices ( ;1)А а , ( 2; )В b and ( ; )С с с .

Determine the intersection point of the median АМ and the line l , if l АМ and С l .

4 Find the equation of the tangent line t to the curve   22 1 2x а c y y   

if q t and :q cx y a b   .

5 Find the rate of      3 21 4 2 5 1g x x c x b x a       ,

i.e. determine where the function is quickly (slowly) increasing (decreasing) .

6 Calculate the limit    0

ln(1 ) lim

. 2 х

x

bx x L

a b c х с 



  

   , if it exists.

7 Determine the constants m and n (if possible),

given that the function  x is continuous in R .

   

3

1

, 1;

, 1;2 ;

ln( 1) , 2.

x

x a m if x

x e b if x

x c n if x

 

    

       

8 Find the gradient of     2; 1 lnbx y bx cx

g x y a xy e y

        

  in point ( ; )А а b .

9 Find the total differential of the multivariable function  ; ; .a by b cxf x y z z y  .

10 Find a function with derivative equal to  

 2 3 ln

tg x bx

ax b x c x x

    .

11 Calculate    3 . sin cosb c x x x a x b x

dx x

    .

12 Evaluate the integral    

21

0

x

cx bx a dx

a b c

 

   .

Deadline 18 Dec 2014 Chief Assist. Prof. PhD Radan Miryanov