Terms of a Sequence Construct a sequence of interpolating values $Y_n,  to,f(1 + \sqrt{10})$, where $f(x) = (1 + X^2)^{-1}$ for 
$-5 \leq X \leq 5$, as follows: For each n = 1,2, ... ,10, let $h = \frac{10} {n}$ 
$x_j^n= -5 + jh$, for each j  = 0, 1,2, ... ,n. 
What would my sequence be exactly.
I have come up with something but it seems incorrect.
The first term would be : $-5+0*\frac{10} {1}$ 
The second ther would be : $-5+1*\frac{10} {2}$
And so forth. But I have a feeling that this is incorrect.
 A: It seems as if you are being asked to use $n$ subintervals (therefore, $n+1$ points) to interpolate the function $f$ on $[-5,5]$. Since the width of the interval is $10$, the width of each subinterval is $h=\frac{10}n$. The mesh for $n$ intervals consists of the points $x_j^n=-5+jh=-5+j\frac{10}n$ for $j=0,1,2,\dots,n$.
For a particular $n$, compute $f(x_j^n)$ for $j=0,1,2,\dots,n$ and interpolate to get $f(1+\sqrt{10})$.
For example, if $n=4$, use the $x$ values $\{-5,-2.5,0,2.5,5\}$ and the $y$ values $\{f(-5),f(-2.5),f(0),f(2.5),f(5)\}$.
The interpolating polynomial is $1-\frac{129}{754}x^2+\frac{2}{377}x^4$ and when that is evaluated at $1+\sqrt{10}$, we get $-\frac1{754}(21+82\sqrt{10})\approx-.3717596394$, which is the fourth value your book gives.
A: You want $11$ equally spaced points from $-5$ to $5,$ which are all the integers:  $-5, -4, -3, \ldots ,5$.  $h$ should be one value, here $1$, which is the spacing of the points.  It should be the length of the interval $(10)$ divided by the number of spaces $(10)$.  I don't know where you got $h=\frac{10}n.$  So it should be $-5+0*1, -5+1*1, \ldots -5+10*1$
