Could anyone help me....

[marajovic126]

2

 

[Deleted member 4993]

Let f(x) = tan(x). What is the formula for the conditioning number of f? Evaluate this formula for x =(π/4), 1.01, 1.26, 1.51 (in radians, working to 3 significant figures, the precision that is implicit in this data). Replace each of the expressions for x by its approximation ^x to 2 significant figures. Compute the relative error of the approximation ^x and the relative error of the approximation f(^x) to f(x).

Note: ^x is x-hat.

Since the question says "working to 3 significant figures, the precision that is implicit in this data" do i need to change π/4 to 3 significant figures and give all my answers once substituted into the formula all to 3 significant figures? Also, im clueless on the second part "Compute the relative error of the approximation ^x and the relative error of the approximation f(^x) to f(x)." any help would be great!

What is the definition of conditioning number of a function?

 

[Bob Brown MSEE]

condition number

In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument. The "function" is the solution of a problem and the "arguments" are the data in the problem. -- wiki

 

[Bob Brown MSEE]

Evaluate this formula for x =(π/4), 1.01, 1.26, 1.51 (in radians, working to 3 significant figures,

I think you are going in the right direction. Build a table.

x0	0.785	1.01	1.26	1.51
x1	0.79	1	1.3	1.5
tan(x0)
tan(x1)
|tan(x0)-tan(x1)|