Содержание
- 2. Question 1. A sequence an, n = 1,2,3,…, satisfies a) Use the definition of limit to
- 3. b) Conclude that and find We have Therefore
- 4. Calculus++ Also known as Hysterical Calculus
- 5. Question 2. A sequence xn, n = 1,2,3,… is and the initial conditions x1 = a,
- 6. Thus, we found two sequences that satisfy the Do any of these sequences satisfy the initial
- 7. Let us check that this linear combination We have Well, we can consider linear combination of
- 8. Thus For the values of arbitrary constants c1 and c2 we obtain Now the limit is
- 9. The method of the week To find the sequence that satisfies the defining relationship and the
- 10. Question 3 a). Find the following limit Solution: We have
- 11. We have The obtained identity yields
- 12. Therefore we can use the following sandwich inequality Since sin x is a continuous function we
- 13. Question 4. State a (positive) definition of a divergent sequence {xn}. Solution: We begin with the
- 14. Question 5. Draw the curve defined by the in the x y – plane. Solution. To
- 15. Now we can find the limit Note the following double inequality Hence
- 16. Since the sandwich theorem tells us that Thus, we have to draw the curve defined by
- 17. Let us look at the xy – plane: y
- 18. The graph of the curve y
- 19. Question 6. Use the definition of convergent sequence to obtain a sandwich inequality for the sequence
- 20. The definition tells us that for all Therefore we obtain the following sandwich inequality for our
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