Ryabushko A.P. IDZ 6.2 option 28

IDZ - 6.2

№ 1.28

Дано: y² = (x-y)/(x+y)

Find the derivatives of y´ and y":

y´ = ((y-x-1)/(y+x+1))^(1/2)

y" = (-2x(y´)^3 - y´)/(2(y²)^(3/2))

№ 2.28

Дано: x = t exp(t); y = t/ exp(t)

Find the derivatives of y´ and y":

y´ = (1-t)/(exp(t))

y" = (-2t+1)/(exp(t))

№ 3.28

Hopefully: y = (7x-4)^6; x0 = 1

Find y‴(x0):

y‴(x0) = 3600

№ 4.28

Hopefully: y = (1+x)/√x

Find the formula for the nth order derivative:

y⁽ⁿ⁾ = (1/2) * ((-1/2)^n) * (x^(-n-1/2)) * ((2n-1)!!) * (1+x)

№ 5.28

Hopefully: y = 4x² – 10x + 13; y = 6x - 7

Find the point at which the curve touches the straight line:

Point (1, 7)

№ 6.28

Given: x = 7(1 - exp(-4t))

Find the reaction rate at time t = 0 s:

The reaction rate at time t = 0 s is 28

In task number 1.28 the function y² = (x-y)/(x+y) is given, you need to find its first and second derivatives. Results: y´ = ((y-x-1)/(y+x+1))^(1/2) and y" = (-2x(y´)^3 - y´)/(2(y²)^ (3/2)).

In task number 2.28 the functions x = t exp(t) and y = t/ exp(t) are given; you need to find their first and second derivatives. Results: y´ = (1-t)/(exp(t)) and y" = (-2t+1)/(exp(t)).

In task number 3.28, the function y = (7x-4)^6 and the value of the argument x0 = 1 are given; you need to find the third derivative of the function y at the point x0. Result: y‴(x0) = 3600.

In task number 4.28 the function y = (1+x)/√x is given, you need to write the formula for its nth order derivative. Result: y⁽ⁿ⁾ = (1/2) * ((-1/2)^n) * (x^(-n-1/2)) * ((2n-1)!!) * (1+x), where !! stands for double factorial.

In task number 5.28 the functions y = 4x² – 10x + 13 and y = 6x - 7 are given, you need to find the point at which the curve touches the straight line. Result: point (1,7).

In task number 6.28, the dependence of the mass of a substance obtained in a chemical reaction on time is given according to the formula x = 7(1 - exp(-4t)). It is required to find the reaction rate at time t = 0 s. Result: the reaction speed at time t = 0 s is 28.

Product description

Ryabushko A.P. IDZ 6.2 option 28

This product is a set of problems and their solutions in mathematical analysis, compiled by A.P. Ryabushko. This version contains problems numbered 1.28, 2.28, 3.28, 4.28, 5.28 and 6.28 from IPD task 6.2. For each problem in the set, its condition and detailed solution are presented with a step-by-step description of the process and the answer.

A set of problems Ryabushko A.P. IDZ 6.2 version 28 is an excellent choice for students and anyone who is interested in mathematical analysis and wants to improve their knowledge and skills in this area.

Ryabushko A.P. IDZ 6.2 version 28 is a set of problems and their solutions in mathematical analysis, created by A.P. Ryabushko. The set contains problems numbered 1.28, 2.28, 3.28, 4.28, 5.28 and 6.28 from IPD task 6.2. Each problem includes its condition and a detailed solution with a step-by-step description of the process and answer. This product is great for students and anyone who is interested in calculus and wants to improve their knowledge and skills in this area. The page is designed in a beautiful html format, which makes the use of A.P. Ryabushko’s set of tasks easy. IDZ 6.2 version 28 is even more convenient and enjoyable.

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Ryabushko A.P. IDZ 6.2 version 28 is a mathematics training task consisting of six problems. In the first problem, you need to find the first and second derivatives of the function y given by the equation y² = (x-y)/(x+y). In the second problem, you need to find the derivative of the function y, given parametrically by the equations x = t exp(t) and y = t/ exp(t). In the third problem, you need to find the third derivative of the function y = (7x - 4)^6 at the point x0 = 1. In the fourth problem, you need to write a formula for the nth order derivative of the function y = (1+x)/√x. In the fifth problem, you need to find the point of intersection of the curve y = 4x² – 10x + 13 with a tangent parallel to the straight line y = 6x - 7. In the sixth problem, you need to find the reaction rate at time t = 0 s, if the relationship between the mass x kg of the substance obtained in a chemical reaction, and time t is given by the formula x = 7(1 - exp(-4t)).

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