Exam papers

on discipline "Higher Mathematics" (VC 96 (3))

Task 1.

Search for:

1. The definite integral using the method of direct integration

2. The indefinite integral using the substitution method

3. The indefinite integral using the method of expansion in partial fractions

4. The indefinite integral using the method of integration by parts

5. The area of \u200b\u200bthe figure bounded by lines.


Task 2.

Dana function of two variables F (x1, x2) = tx1 + 2x2, which is performed under the conditions:


1. Show graphically the range of permissible values \u200b\u200bof this function. Record any admissible values \u200b\u200bof the variables and find the value of the function for these values

2. Find the maximum and minimum values \u200b\u200bof this function under prescribed conditions.

3. Under this condition specify the basic problem of linear programming. Then write it in standard form and canonical form.

4. Write down the problem to the dual problem of the preceding paragraph.

5. Determine the solution of the dual problem.



Task 3.

Marketing service company conducted a sample study of prices for goods and the market and shops in the city. The price of 3.9 thousand. T rubles met again, the price of 4 thousand. Rub. - T + 3 times the price of 4.1 thousand. Rub. - T + 5 times, while the price of 4.2 thousand. Rub. - T + 1 times.


1. Locate the statistical probability of each option prices for the goods and make a study of the probability distribution table, assuming that the price - it is a random variable.

2. Construct a polygon probability of generating random numbers.

3. Write down the probability distribution function and build her schedule.

4. Find the mean and variance. Describe the meanings of the numbers obtained.

5. Father and son independently at the same time bought the goods A. How many versions of this pair might buy? All these options are equally?

The work was put on 5.Proveryaet teacher Maslova !! - required modification work.