Ryabushko A.P. IDZ 6.2 version 11

IDZ-6.2

Below are the challenges and solutions:

№ 1.11

Know: y = eʸ+ 4x

Find the derivatives of y´ and y".

Answer:

Let's apply the rule for differentiating a complex function:

y´ = (eʸ+ 4x)´ = (y´eʸ+ 4) = eʸ+ 4

Let's differentiate the resulting expression:

y" = (eʸ+ 4)´ = y"eʸ

№ 2.11

Given: x = eᵗ cos t; y = eᵗ sin t

Find the derivatives of y´ and y".

Answer:

Let's find the derivatives of x and y:

x´ = eᵗ cos t - eᵗ sin t

y´ = eᵗ cos t + eᵗ sin t

Let us differentiate the resulting expressions:

x" = eᵗ cos t - 2eᵗ sin t

y" = eᵗ cos t + 2eᵗ sin t

№ 3.11

Hopefully: y = arcsin x; x0 = 0

Find the third derivative y‴(x0).

Answer:

Let's differentiate the function y:

y´ = 1/√(1-x²)

Let's differentiate the resulting expression:

y" = x/((1-x²)^(3/2))

Let's differentiate again:

y‴ = (1-x² - 2x²)/((1-x²)^(5/2))

I set x0 = 0:

y‴(0) = -2/√1 = -2

№ 4.11

Hopefully: y = 1/(x-3)

Write down the formula for the nth order derivative.

Answer:

Let's apply Leibniz's rule for the derivative of a product:

y⁽ⁿ⁾ = ((-1)ⁿn!)/(x-3)^(n+1)

№ 5.11

Given: y = x²/4 – 27x + 60; x = 2

Find the equation of the normal to the curve at the point with abscissa x = 2.

Answer:

Let's find the value of the function y at the point x = 2:

y(2) = 2²/4 - 27·2 + 60 = -46

Let's find the value of the derivative of the function at the point x = 2:

y´(2) = 2/2 - 27 = -26

The equation of the normal to the curve at point (2, -46) has the form:

y + 46 = (-1/(-26))(x - 2)

Let's simplify:

y = (-13x/13) - 11

№ 6.11

Given: S = 5t³/3 - t²/2 + 7

Find the time when the speed of the material point is 42 m/s.

Answer:

Let's find the derivative of S with respect to time:

v = S´ = 5t² - t

To find the time when the speed is 42 m/s, solve the equation:

42 = 5t² - t

Let's bring the quadratic equation to its general form:

5t² - t - 42 = 0

Let's solve it using the discriminant formula:

t = (-(-1) ± √((-1)² - 4·5·(-42)))/(2·5) = (1 ± √421)/10

Since we are looking for time, we will choose a positive root:

t ≈ 1.796 sec

Ryabushko A.P. IDZ 6.2 version 11

This digital product is a set of mathematical analysis problems completed by student A.P. Ryabushko. as part of individual homework 6.2. This version presents problems No. 1.11-6.11, which cover various topics from mathematical analysis, such as differentiation, finding derivatives, normal equations, etc.

Each problem contains a detailed description and a complete solution, which is made in compliance with all the rules of mathematical notation and is clear and easy to read. In addition, each solution is beautifully designed in HTML format, making it even more attractive and easy to read.

This product is ideal for students and teachers of mathematical specialties, as well as for anyone who is interested in mathematical analysis and wants to improve their knowledge in this area.

Don't miss the opportunity to purchase this digital product and improve your knowledge of calculus!

Ryabushko A.P. IDZ 6.2 version 11 is a set of problems in mathematical analysis completed by student A.P. Ryabushko. as part of individual homework 6.2. This option presents six problems that cover various topics from calculus such as differentiation, finding derivatives, normal equations, etc.

Each problem contains a detailed description and a complete solution, executed in compliance with all the rules of mathematical notation and being clear and easy to read. In addition, each solution is presented in HTML format, which makes it even more attractive and easy to read.

This product is ideal for mathematics students and teachers, as well as for anyone who is interested in mathematical analysis and wants to improve their knowledge in this area. Purchasing this digital product will help you improve your calculus skills and solve complex problems with more confidence. If you have any questions, you can contact the seller listed in the seller information.

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Ryabushko A.P. IDZ 6.2 version 11 is a textbook that contains tasks and solutions on mathematical analysis and differential equations. This manual presents various problems, such as finding derivatives, solving equations, writing formulas for nth order derivatives, as well as problems on geometry and the laws of motion of a material point. All assignments are provided with detailed solutions, which allows you to more deeply understand the material and prepare for exams. If you have any questions, you can contact the seller listed in the seller information.

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