Question

finding magnitude of error?

Answer 1

This is asking for the maximum remainder of the 1st Maclaurin Polynomial of sin(x).
By the Lagrange Error Definition, \[\left| R_n(x) \right| \le \max_{[x,c]} \left|f^{(n+1)}(z)\right|\frac{\left|(x-c)^{n+1}\right|}{(n+1)!}\]
This is an incredibly ugly formula. Let's separate it into chunks.
The first part, \(\max_{[x,c]} \left|f^{(n+1)}(z)\right|\) is asking for the maximum value of the next derivative (here, the second derivative) on the interval (0,1.3). For sin and cos, we usually just say it is 1.
For the rest of it, \(\frac{\left|(x-c)^{n+1}\right|}{(n+1)!}\), we just have to plug in x=0, c=1.3, and n=1.
Basically we have 1 for the first part and the numbers to plug in to the second part. You should get 1.3/2 = .65
What's more important, though, is that you understand my reasoning. Do you get my thought process?

Answer 2

noits very confusing... but it wants the answer rounded to one decimal place so i put 0.7 and it said its wrong

Answer 3

i dont understand the first part, because of the interval part

Answer 4

i used the method 1.3-sin1.3 = 0.33644181458 , and so it is less than 0.4 ( 0.4 was the answer) :) ty