# Higher Mathematics, option 5

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1. Find the limit:.
2. Find the derivative and differential of a function:.
3. Determine the intervals of increase and decrease, as well as the maximum and minimum:.
4. Evaluate the integral:.
5. Find the area bounded by the graph of the function and direct:,.
6. The coordinates of a curve are related by the equation:. Find the equation of the curve when it passes through the point:,.

Problem 1. In the cell 6 and 4 white gray mouse. Randomly extracted 3 mice. Calculate the probability of drawing the mice of the same color.

Problem 2. What probably win pro¬tivnika y is equivalent to four parties of five or seven of the nine?

Problem 3. A random variable X is given plotno¬sti probability function:
Find the expectation value of H.

Task 4. Method ANOVA with a significance level P = 0.05 to verify drug efficacy feedback factor (F) by the value of blood pressure (mm. Hg. V.) On the experimental results shown in the table.
Experience number 30 F1 = F1 = F1 = 100 60 F1 = 150
1 180 160 140 120
2 200 170 150 130
3 170 150 130 110

Task 5. To determine the efficacy of a pre¬parata explore some vital signs in the animals of the two groups. The average value of this indicator for the 14 animals of the experimental group (ie the group which primenyal¬sya drug) was x = 6.0 when the corrected sample variance sx2 = 0,0100; For the 12 animals in the control group were found to be indicators so¬otvetstvuyuschie y = 5.5 and sy2 = 0,0144.
The assumption that the normal distribution of the studied index zako¬na animals like opyt¬noy and control groups at a significance level of p = 0.05 to determine:
a) significantly different results if the dispersion corrected vybo¬rochnye sx2 and sy2 (when competing hypotheses, sostoya¬schey in the statement of the inequality of the relevant general dispersions);
b) significantly differ if found mean values \u200b\u200bof the studied index for the two groups of animals. Iny¬mi words, allow you utverzh¬dat studies that this drug does have opredelen¬noe impact on the studied parameters of animal?