MIREA. The Moscow State Institute of Radio Engineering, Electronics and Automation (Technical University). E-book (DjVu-file) contains 20 tasks for solving mathematical analysis of the model calculation of the divisions of mathematical analysis (theory of limits and differential calculus), which came into the program I semester of full-time faculty of the Navy and Cybernetics. Tasks are taken from the collection of common tasks for students MIREA. Compilers; A.G.Aslanyan, N.V.Beletskaya, I.P.Dragileva, YI simple. I.P.Frolov. Yu.I.Hudak Editor (Publisher MIREA 2009). Option-26.
Solving problems presented in the form of a scanned handwriting collected into a single document of 19 pages. This document is stored in a format DjVu, which is opened in the Internet Explorer or Mozilla Firefox after installing utility program (plug-in). Link to download and install DjVu-plug attached. DjVu-file that contains the conditions of problems and their detailed solutions, ready for viewing on your computer and print. All tasks were successfully offset MIREA teachers.
Exercises model calculation:
TASK 1. Using the definition of a limit order to show that this sequence u_p as n → ∞ has as its limit the number of A. Find an integer N, from which | u_n - A | <ε.
GOAL 2. Calculate the limit.
GOAL 3. Calculate the derivative y '(x).
OBJECTIVE 4. Calculate the derivative y '(x).
PROBLEM 5. Calculate the logarithmic derivative y '(x).
OBJECTIVE 6. Calculate the derivative y '(x) function given parametrically.
GOAL 7. Calculate the derivative y '(x) function defined implicitly by the equation f (x, y) = 0.
Problem 8. Find the limit, using the rule of L'Hospital.
Problem 9. Find the limit, using the rule of L'Hospital.
Task 10. The function y = f (x) expanded by Taylor's formula in a neighborhood of x0 to o ((x-x0) ^ n).
Problem 11. Calculate the limit of two ways a) using the expansion of the Taylor formula, b) using L'Hopital's rule.
Problem 12. Construct a graph of the function y = (ax ^ 3 + bx ^ 2 + cx + d) / (x ^ 2 + px + q).
Problem 13. Construct a graph of the function y (x).
Problem 14. Construct a graph of the function.
Problem 15. Construct a line given by the equation ρ = f (φ) in polar coordinates (ρ≥ 0, 0≤φ≤2π).
GOAL 16, 17. Calculate the approximate values \u200b\u200bindicated.
Problem 18. Calculate the partial derivatives of the first order.
Problem 19. Calculate the mixed second derivatives and ensure that they are equal.
Problem 20. Find and explore the extremum point.