*39. If x < y, prove that x < t my < y. *40. If x > 0 and y > 0, prove that xy = 47. (Hint: Use the fact that (Vx - V9)>

[answerhappygod]

39 If X Y Prove That X T My Y 40 If X 0 And Y 0 Prove That Xy 47 Hint Use The Fact That Vx V9 1 (181.52 KiB) Viewed 81 times

*39. If x < y, prove that x < t my < y. *40. If x > 0 and y > 0, prove that xy = 47. (Hint: Use the fact that (Vx - V9)> 0.] *41. If 0 < a <b, prove that 0 < a> <b2 and 0 < Va< . 42. If x, y, a, and b are greater than zero and < , prove that * < * < g. 43. Let A = {r:r is a rational number and r <2}. Prove that A has no largest member. (Hint: If x2 < 2, and r > 0, choose a rational number 8 such that 0 < 8 < 1 and 8 < 2,1 Show that (r + 8)2 < 2.] 2 + *44. If x = supS, show that, for each e > 0, there is a ES such that x - € < a < x. *45. If y = infS, show that, for each e > 0, there is a ES such that y Sa<y+ €.