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Agitayeva K.N. EE-14-1

Task 1. Given function f(x) and a point x=a.

1. Compute the two-sided limit of the function at the point indicated;

2. Calculate the left-sided limit at the point indicated;

3. Calculate the right-sided limit at the point indicated;

4. Conclude that the discontinuity of the function at x=a and type of fracture.

Implementation of the task

Continuous

Task 2. Calculate the function f(x):

1. f’(x);

2. f’(x₀);

3. f’’(x);

4. f’’(x₀).

Implementation of the task

Task 3. Draw the graph of the function

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Task 4. Plot parametrically given function f(x).

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Task 5. Draw the graph of polar coordinates.

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Task 6. Draw the graph of the function y=f(x) in the Cartesian coordinate system. Built in the same coordinate system tangent and normal function of this at the specified point.

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Task 7. Show graph of this function, find the derivative, find the zeros of the derivative (stationary points), find the coordinates of extreme points.

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Task 8. Three-dimensional surface plot.

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Task 1. Calculate the indefinite integral and check calculations differentiation. Construct a graph of a family of three primitives

Implementation of the task

Designation through the 1^st derivative F(x)

Graph of three primitives

Task 2. Calculate the definite integral

Implementation of the work

Task 3. Find image of function (Laplace transform)

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Task 4. Find the original of given functions (Inverse Laplace transform)

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Task 5. To solve differential equation with operatonal calculus (Laplace transform)

Inplementation of the task

Task 6. . To solve system of differential equation with operatonal calculus

Task 7. To solve system of differential equation with command Given/Odesolve. Initial conditions are similar for all given variants. To create table of arguments and interpretation of function. To construct graph of obtained functions. To construct phaseous figure.

Implementation of the work

Task 8. To solve system of differential equation with command rkfixed. Initial conditions are similar for all given variants. To create table of arguments and interpretation of function. To construct graph of obtained functions. To construct phaseous figure.

Implementation of the work