MATH 255 Midterm: MATH255 Winter 2001 Exam

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 255
• Professor: All

Document Summary

Justify your answer. (i) (5 marks) (ii) (5 marks) (iii) (5 marks) (iv) (5 marks) n2 + 1 sin(cid:18) . 3. (i) (4 marks) de ne the term riemann partition. (ii) (4 marks) de ne the upper and lower riemann sums u(p, f) and l(p, f) for a. Let f : [0, 1] [ 1, 1] be de ned by f(x) = ( 1)k if x ]2 (k+1), 2 k] and f(0) = 0. (iii) (8 marks) given > 0 nd explicitly a riemann partition p of [0, 1] with. What is the signi cance of what you have just shown? (iv) (4 marks) what is the value of r 1. 0 f(x)dx: for each of the following sequences of functions de ned on ]0, [ determine the point- wise limit. Determine also whether convergence is uniform on ]0, [. Justify your answer. (i) (10 marks) fn(x) = nx n x .