Скачать или смотреть SOLUTIONS TO EXERCISE 4.2 | Q1-Q5 | PART 1 | REAL ANALYSIS | BARTLE & SHERBERT

In this video solutions to Q1 to Q5 of Exercise 4.2 of Introduction to Real Analysis book by Bartle and Sherbert are provided. Solutions to Q6 to Q10 will be provided in Part 2 and Q11 to Q15 in Part 3 of this video.

LINK OF PART 2:    • SOLUTIONS TO EXERCISE 4.2 | Q6 - Q10 | PAR...  
LINK OF PART 3:

Theory of Real Functions
Bartle & Sherbert
Real Analysis
B.SC (H) Mathematics Sem III
University of Delhi


1. Apply Theorem 4.2.4 to determine the following limits:

2. Determine the following limits and state which theorems are used in each case. (You may wish to use Exercise 15 below.)

3. Find

4. Prove that lim cos( 1/x) does not exist but that lim x cos(1/x) = 0.

5. Let f, g be defined on A subset of R to R, and let c be a cluster point of A. Suppose that f is bounded on a neighborhood of c and that lim g = 0. Prove that lim fg = 0.