Part I Limit of a Punction 3-1 Coder the tollovtng fmetion: e) 1. What is the do

Question

Part I Limit of a Punction 3-1 Coder the tollovtng fmetion: e) 1. What is the domain of the funetion? Is there any point where the function is not defined, and why? 35-1 Below is the graph of the function f() The funetion appears to have Thole" whore the curve croNos the y-axis. If you look carefully, the "hale" appesns to be above the point (0,1) an the y-axcis 2. Complete the tables below to get approximate coordinates of the "hole" shown above. To do so, evaluate the function for z-values that are increasingly chm tr = 0, on the right and on the lef, rounded to three decimal places 0.1 0.01 0.001 0.0001 0.00001 f(r) 0.1 0.0 0.001 0.0001 000001 f(r) 3. Based on the table values, what are the approximate coordinates of the "hole"?

Explanation / Answer

2.when x=1, f(x) =31-1/1 =2

When x=0.1, f(x) =(30.1-1)/0.1=1.16

when x=0.01, f(x) =(30.01-1)/0.01 = 1.10467

when x=0.001, f(x) =(30.001-1)/0.001=1.0992

when x =0.0001, f(x) =30.001-1/0.0001= 1.0987

when x=0.00001, f(x) =30.00001-1/0.00001=1.0986

when x=-1, f(x)=(3-1-1)/-1 = 0.6667

when x=-0.1, f(x)=1.04

When x=-0.01, f(x) = 1.0926

when x=-0.001, f(x) =1.098

when x=-0.0001, f(x) =1.09855

when x=-0.00001, f(x) = 1.0986

3. As we see that when x approaches to 0 from both sides, f(x) approaches to 1.

So the hole is at x=1 .

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