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Kozhaniyazov.D.A 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

x = 4

Task 2. Calculate the function f(x):

x = 0

1. f’(x);

2. f’(x₀);

3. f’’(x);

4. f’’(x₀).

Implementation of the task

Task 3. Draw the graph of the function

Implementation of the task

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

Implementation of the task

Task 5. Draw the graph of polar coordinates.

Implementation of the task

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.

x0 = -1

Implementation of the task

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

Implementation of the task

Task 8. Three-dimensional surface plot.

Implementation of the task