I request you to please send me the step-by-step solution for the below theorems... Needed to be solved clearly, please... Needed a brief explanation... Theorem. Let a be an irrational number. Then there ezist in finitely many distinct rational numbers : forwhich r-<• Since q grows much more quickly than 2q, this gives us better approximations with smaller denom-inators.

First prove a the following lemma: If n≥1be any integer, then there exists a rationa number pqsuch…

Answered: Theorem. Let z be an irrational number.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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IV 2 Solve the following inequalities algebraically. Express your answer using interval notation. a) 2x-5 x + 1 2x + 3 x + 4 f) x - 2 c) ハx-5 3 4
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Solve and graph the given inequalitie
i am stuck with a question where I need to prove the following: (1+||x+y||)≤(1+||x||)(1+||y||) I know I need to simplify the right side, but from there I am lost, I see solutions where ||x||||y|| is ignored because its greater than or equal to zero, but I dont get why we ignore ||x||||y|| but not ||x||+||y||, if able please give the proof with explanation I would be very thankful
Evaluate the following.a. ∫ √ (1+x2) from x=0 to x=√7Please show complete solution. Thank you so much.
1.3) Use geometric interpretation to explain whether the following set of equations will have infinitely many solutions, no solution, or a unique solution: f([x;y])=[5;-5] f([x;y])=[0;0] this is all the info I get and I am confused on how to appraoch this
Please answer the following questions (i): Are −3 and −2 solutions to x2 – x – 12 ≤ 0? (ii): − x2 + 4x + 5 ≥ 0 (iii): (a) The discriminant is always less than 0 in quadratic inequalities True/False

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Theorem. Let z be an irrational number. Then there exist in finitely many distinct rational numbers for which z-< Since q² grows much more quickly than 2q, this gives us better approximations with smaller denom- inators.