Computing Percent Error in Linear Approximations...

[StintedVisions]

We went over this section last week and the professor only covered half of it. I've got most of the answers except how to calculate the percent error. The question is:

Use the following function to complete sections a-d.

f(x)= x / x+2 ; a=1; f(1.1)


I've gotten so far as to
a) f(x)~L(x)=(1/3)+(2/9)(x-1)
b) was graphing, I got the graph correct
c) f(1.1)~.356

everything above was correct, however part d) is computing the percent error. The formula is given 100*|(approx-exact)/exact|, I tried to compute it anyway and what I got and what the correct answer was were very different. Can anyone point me in the proper direction?

 

[Deleted member 4993]

We went over this section last week and the professor only covered half of it. I've got most of the answers except how to calculate the percent error. The question is:

Use the following function to complete sections a-d.

f(x)= x / x+2 ; a=1; f(1.1)


I've gotten so far as to
a) f(x)~L(x)=(1/3)+(2/9)(x-1)
b) was graphing, I got the graph correct
c) f(1.1)~.356

everything above was correct, however part d) is computing the percent error. The formula is given 100*|(approx-exact)/exact|, I tried to compute it anyway and what I got and what the correct answer was were very different. Can anyone point me in the proper direction?

Given equation is correct.

Please show your work and answer

- and we will be able to tell then if and where you might have taken the wrong path.

 

[StintedVisions]

I did |(.356-1.1) / 1.1| * 100 and got 67.636.

I don't know what to put in for exact and approximate values. That was just my stab at it.

 

[HallsofIvy]

You are subtracting the value of x from the value of f(x). Those are NOT "exact" and "approximate" values of f(x). Your exact value should be the value of f(1.1)= 1.1/(1.1+ 2)= 1.1/3.1= 11/31. Your approximate value should be the value you get using that linear approximation, 1/3+ (2/9)(1.1- 1)= 3/9+ .2/9= 3.2/9= 32/90.