y

y

>

, suppose that there is a number

N>0

so that the implication below is true:\

if x>N, then |(1)/(2x-5)|

\ a. If

\\\\epsi =0.1

, find the largest value for

N>0

which ensures the above implication is true.\

N=

\ b. If

c=0.01

, find the largest value for

N>0

which ensures the above implication is true.\

N=

\ c. Using the work you did in parts

a

, and

b

, find the smallest value for

N>0

which ensures the above implication is true for an arbitrary

2>0

. (Your answer should be an expres

N=

\ C. The resuz you found in part c. proves that a certain limit exists. Fill in the blanks below for the pieces of the corresponding limit.\ The value, is approaching is

a=

\ i. The function is

f(x)=(1)/((1)/(2x-5))

>0, suppose that there is a number N>0 so that the implication below is true: ifx>N,then2x510 which ensures the above implication is true. N= b. If c=0.01, find the largest value for N>0 which ensures the above implication is true. N= c. Using the work you did in parts a, and b, find the smallest value for N>0 which ensures the above implication is true for an arbitrary 2>0. (Yaur answer should be an expre e. The resuz you found in part c. proves that a certain limit exists. Fill in the blanks below for the pieces of the corresponding limit. 1. The value x is approsching is a= 1. The function is f(x)=2x51