Control №8 and 9 in higher mathematics, option 6

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Uploaded: 03.09.2013
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Option 6
Examination №8
Target 8.1.
D'Alembert's method to find the solution of free vibrations of an infinite string, if initially the form of the string and the speed of the string with abscissa x is determined accordingly and given functions.
Construct a graph of the function u (x, t) at t = 0.
Task 8.2
Dana function. Find its significance at a point.
Task 8.3
Present given function, where, in the form. Check whether it is analytical. If so, find the value of its derivative at a given point.
Task 8.4
Operating method to find a particular solution of the differential equation satisfying the given initial conditions.
,,,.
Task 8.5
Check whether the vector field potential and solenoidal. In the case of a potential field to find his potential.

Examination №9
Task 9.1
On the cards are drawn letters: B, D, E, E, P, P, P, T, and U.
What is the probability that a random arrangement of cards in a row will PETERSBURG word.
Task 9.2
There are three communication lines. The probability that they are engaged, are respectively equal to 0.15; 0.4 and 0.5.
What is the likelihood that the active point at least one of them is free.
Task 9.3
The probability of having a boy is 0.51. The family of five children.
What is the probability that a boy in a family of 4?
Not less than three boys?
What is the most probable number of boys?
Task 9.4
The apparatus consists of 2,000 elements operating independently of one another. The probability of failure of any element of a period of time T is equal to 0.002. Find the probability of failure during three or more T cells.
Task 9.5
Create the distribution law of the random variable X. Find the expectation, variance and standard deviation of the random variable X. Find the probability of events A, B, C.
Dice thrown 4 times. The random variable X - the number of sixes fallout. The event A is that, in the event consists in that X <2, event C is that.
Task 9.6
Dana function, where a - option. Find a value and that the function has the density of the probability distribution. Calculate the expectation, variance, standard deviation of the random variable X. Find the probability of events A, B, C.
A: A <0, B:, C:.

Additional information

The exact formulation of the tasks you can see in the attached image

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