Problems

In Problems 1-40, assume that: ε, δ are positive infinitesimal, H, K are positive infinite. Determine whether the given expression is infinitesimal, finite but not infinitesimal, or infinite.

(Hint: Assume ε > 5 and divide through by ε.)

41            In (a)-(f) below, determine which of the two numbers is greater,

(a) ε or ε² 

(b) or

(c) H or H²

(d) ε or √ε

(e) H or √H

(f) √H or

42            Let x, y be positive hyperreal numbers. Can be infinite? Finite? Infinitesimal?

43            Let a and b be real. When is (3ε² - ε + a)/(4ε² + 2ε + b)

(a)  infinitesimal?

(b)  finite but not infinitesimal?

(c)  infinite?

44            Let a and b be real. When is (aH² - 2H + 5)/(bH² + H - 2)

(a)  infinitesimal?

(b)  finite but not infinitesimal?

(c)  infinite?