Functions/Linear interpolation/Errors & % of errors - Hmwk help?

Question

For the function f(x)=sqr root (x) we know f(4)=2 and f(9)=3.
(a) Use linear interpolation to find sqr root of 5
(b) Find the error to 3 decimal places using a calculator or sqr root table.
(c) What is the percentage error? (Recall that percentage error is 100*error/(exact answer).)

Thanks for the help...I think I got a and b but even with the formula laid out I can't seem to get c. So I figure maybe I better see the whole thing worked out.

Answer 1

(a) The points given in the xy-plane are (4,2) and (9,3) the slope is (3-2)/(9-4) = 1/5. So, for our linear interpolation we can assume f(x) = sqrt(x) is approximately f(x) = x/5 +6/5
For x = 5, we approximate this to 11/5, or 2.200

(b) I assume the error sought in this part is the absolute error, which is the absolute value of (estimated value - actual value) So, abs(2.200-2.236) = 0.036

2.200 is your linear approximation and 2.236 is the calculator approximation to three decimal places of the square root of five.

(c) using the formula provided in your question: 100*0.036/2.236 = 1.610%

Answer 2

Let's say, linear interpolation gives you one answer.
You know the EXACT answer is something else.

Here, you have the difference, correct? Subtract one from the other to get this difference.

Now, get the fractional figure of this DIFFERENCE over what is the EXACT answer. You'll get a fraction. Multiply this by 100 to get the percentage.

Answer 3

My dad works contained in the IT branch (works on each and every of the pcs) at a school and he has those each and every of the time, at the same time as he first instructed me what it changed into i did not get it, then i have been given it and that i requested him if he from time to time wrote that down for what changed into incorrect and he reported on occasion he did!

Answer 4

(a)
5 - 4 = 1
9 - 4 = 5
3 - 2 = 1
1*1/5 = 0.2
2 + 0.2 = 2.2
(b)
√5 ≈ 2.236
ε ≈ 2.236 - 2.2 ≈ 0.036
(c)
%ε ≈ 100*0.036/2.236 ≈ 1.610%