MATH 255 Midterm: MATH255 Winter 2004 Exam

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

Document Summary

1. (i) (10 marks) state and prove the cauchy schwarz inequality (ii) (10 marks) let a1, a2, . 1 or otherwise, show that a1 + a2 + + an 1 + an a2. 3 + + a2 n 1a 1 n + a2 na 1. 2. (i) (6 marks) describe riemann"s criterion for integrability. (ii) (7 marks) If f is a riemann integrable function on [0, 1] show that the function. |f | de ned by |f |(x) = |f (x)| is also riemann integrable on [0, 1]. (iii) (7 marks) let g(x) = . 1 q if x is irrational, if x = p q in lowest terms with p and q integers. 3. (i) (5 marks) let f (x) = ex. 1 + nx2 . fn(x) = cos(nx2). fn(x) = x. Mathematics math255: let an > 0 and.