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Higher Mathematics for external students of  biological faculty

1st semester
 

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Topics

Variants

MW

Σ

Date

01

Given two vectors  `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` and `#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` . Find:  

:: 1 :: the coordinates of  `#mover(mi("m",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` = 3*`#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))`-2*`#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))`  

:: 2 :: unit vector for `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` 

:: 3 :: the scalar product of vectors `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` and `#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` 

:: 4 :: the angle between the vectors `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` and `#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` 

:: 5 :: vector product `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` and `#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))`  
:: 6 :: area of ??the parallelogram constructed on the vectors `#mover(mi("a",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))` and `#mover(mi("b",fontweight = "bold",mathcolor = "maroon"),mo("→",fontweight = "bold",mathcolor = "maroon"))`.

 

 

02

Solve the system by Cramer's rule

 

 

 

03

Solve the system using Gauss-Jordan method

 

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04

Given the triangle ABC:  A(x[A];y[A]) , B(x[B];y[B]) and C(x[C];y[C]).  Find:

 :: 1 :: The equations of sides AB and AC;

 :: 2 ::  height equation CH;

 :: 3 :: the equation and the median length of AM;

 :: 4 :: the angle BAC;

 :: 5 :: equation of a line passing through the vertex C, parallel to side AB;

 :: 6 ::point of intersection of the median AM and the height CH;

 :: 7 :: area of ??triangle ABC;

 :: 8 :: make a drawing.

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05

Discover which line is determined by this equation, bring it to its simplest form, make a drawing.

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06

Find the limit of a rational function at infinity

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07

Find the limit of a rational function at a point of discontinuity

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08

Find the limit of irrational functions

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09

Calculated using the first remarkable limit

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10

Calculated using the second remarkable limit

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11

Find the derivative of composite functions

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12

Find the derivative of the quotient

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13

Find the derivative of the product

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14

Explore means of differential calculus entire rational function and to build its graph

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15

Explore means of differential calculus rational function and to build its graph

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