Question

The function f changes value when x changes from a to a + dx. Find the appoximation error. F(x) = x^3, a =8, dx = 0.05

Answer 1

what does u mean by x^3 ???
x*3 or x/3

Answer 2

F with exponent 3

Answer 3

Do u know how to solve?

Answer 4

u have to take the cube of x

Answer 5

Yes what is x

Answer 6

As u said above that the value of x changes from a to a+dx So according to the given value x will be 8.05

Answer 7

Ok my options for the answer are as following

Answer 8

0.12025

Answer 9

0.0300625

Answer 10

0.09010875

Answer 11

Or 0.060125

Answer 12

I think 0.12025

Answer 13

I think I am answering something else
your question is not, what I am thinking

Answer 14

Are u sure, cuz this is actually on a test im taking

Answer 15

You should wait for someone else to answer it

Answer 16

Ha okay

Answer 17

The exact answer is to take the derivative:

F'(x) = 3x^2
F'(8) = 3*8^2=3*64=192

So now let's approximate:

(F(8+.05) - F(8)) / .05 = ((8+.05)^3 - 8^3) / .05 = 193.2025

So the error in this approximation method is:

(192 - 193.2025)/192 = -0.0062630208333...

This is a pretty small!