IDZ Ryabushko AZ 6.4

IDZ Ryabushko AZ 6.4

Classroom Assignment Ryabushko - 6.4

Classroom assignment in higher mathematics, section 6.4.
Section: Chapter 6. Differential Calculus of Functions of One Variable and Its Applications
Topic: Higher order derivatives
Description: Finding second and higher order derivatives of explicit, parametrically defined and implicit functions, calculating the values of derivatives at given points, finding the velocity and acceleration of a point from the law of motion, writing the equations of the tangent line and the normal to a curve, checking that a function satisfies a given differential equation.

Tasks:
1. Find the second derivative of the function
2. Find the values of derivatives of any order of the function at a given point
3. Using the given law of motion of a point, find the velocity and acceleration at given instants of time
4. Find the second derivatives of functions defined parametrically
5. Calculate the value of the second derivative of a function defined implicitly at a given point
6. Write the equations of the tangent line and the normal to the curve at the point M0(2; 2)
7. Show that the function satisfies the given equation for any constants

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• Complete solution of all 7 tasks of the variant
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• All formulas and calculations
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