Let = the load factor n/m. Theorems 11.6 and 11.8 establish the upper bounds of 1/(1 ) and (1/)ln(1/(1)) on the expected number of probes in unsuccessful and successful search, respectively. Fill in the following table by values of these upper bounds for the given values of . Show the values to four decimal places.

	1/(1 )	(1/)ln(1/(1))
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.99
0.999

Determine the value of each of the following:

lim₀1/(1 )

lim₁1/(1 )

lim₀(1/)ln(1/(1))

lim₁(1/)ln(1/(1))

2. Let the load factor nm. Theorems l 1.6 and 11 8 establish the upper bounds of id ) and (1 In 1/ 1-c) on the expected number of probes in unsuccessful and successful search, respectively a. Fill in the following table by values of these upper bounds for the given values of . Show the values to four decimal places 1/(1-) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 359 0.99 0.999 b. Determine the value of each of the following: i, linn,-01/(1-a) ii. lima-/(I -a) iii. lima.-0(1/)ln(1/(1-)) iv. Iim,-.i(1/)ln(1/(1-a))