Higher mathematics option 3
Replenishment date: 18.12.2013
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Exam assignments
in the discipline "HIGHER MATHEMATICS" (VK 96 (3))
Task 1.
Find:
1. A definite integral using the direct integration method
2. Indefinite integral using the substitution method
3. Indefinite integral using the method of expansion into simple fractions
4. Indefinite integral using the method of integration by parts
5. The area of the figure bounded by lines.
Task 2.
A function of two variables F (x1, x2) = tx1 + 2x2 is given, which is fulfilled under the conditions:
1. Show graphically the range of valid values of this function. Write down some valid variable values and find the value of the function at these values
2. Find the maximum and minimum values of this function under the given conditions.
3. Under this condition, formulate the main linear programming problem. Then write it down in standard and canonical form.
4. Write down the problem dual to the problem from the previous paragraph.
5. Determine the solution to the dual problem.
Task 3.
The marketing service of the company conducted a sample study of the price of product A in the markets and shops of the city. The price of 3,9 thousand rubles was met t times, the price was 4 thousand rubles. - t + 3 times, price 4,1 thousand rubles. - t + 5 times, and the price is 4,2 thousand rubles. - t + 1 times.
1. Find the statistical probability of each variant of the price for the product under study and draw up a table of the probability distribution, assuming that the price is a random variable.
2. Construct a polygon of probabilities of the resulting random variable.
3. Write down the probability distribution function and plot it.
4. Find the expected value and variance. Describe the meaning of the numbers obtained.
5. Father and son, independently of each other, simultaneously bought item A. How many options for such a pair purchase are possible? Are all of these options equally likely?
in the discipline "HIGHER MATHEMATICS" (VK 96 (3))
Task 1.
Find:
1. A definite integral using the direct integration method
2. Indefinite integral using the substitution method
3. Indefinite integral using the method of expansion into simple fractions
4. Indefinite integral using the method of integration by parts
5. The area of the figure bounded by lines.
Task 2.
A function of two variables F (x1, x2) = tx1 + 2x2 is given, which is fulfilled under the conditions:
1. Show graphically the range of valid values of this function. Write down some valid variable values and find the value of the function at these values
2. Find the maximum and minimum values of this function under the given conditions.
3. Under this condition, formulate the main linear programming problem. Then write it down in standard and canonical form.
4. Write down the problem dual to the problem from the previous paragraph.
5. Determine the solution to the dual problem.
Task 3.
The marketing service of the company conducted a sample study of the price of product A in the markets and shops of the city. The price of 3,9 thousand rubles was met t times, the price was 4 thousand rubles. - t + 3 times, price 4,1 thousand rubles. - t + 5 times, and the price is 4,2 thousand rubles. - t + 1 times.
1. Find the statistical probability of each variant of the price for the product under study and draw up a table of the probability distribution, assuming that the price is a random variable.
2. Construct a polygon of probabilities of the resulting random variable.
3. Write down the probability distribution function and plot it.
4. Find the expected value and variance. Describe the meaning of the numbers obtained.
5. Father and son, independently of each other, simultaneously bought item A. How many options for such a pair purchase are possible? Are all of these options equally likely?