I want to know how to solve this problemSolutionTo understan

I want to know how to solve this problem.

Solution

To understand this problem there is One method of interpolation ,

Using inetpolation theorm we can solve is , example of interpolation is as below.

Following is a table of values for f (x) =

tan x for a few values of x.

x 1 1.1 1.2 1.3

tan x 1.5574 1.9648 2.5722 3.6021

Use linear interpolation to estimate tan(1.15). Then

use

x0 = 1.1, x1 = 1.2

with corresponding values for y0 and y1. Then

tan x y0 +

x x0

x1 x0

[y1 y0]

tan x y0 +

x x0

x1 x0

[y1 y0]

tan (1.15) 1.9648 +

1.15 1.1

1.2 1.1

[2.5722 1.9648]

= 2.2685

The true value is tan1.15 = 2.2345. We will want

to examine formulas for the error in interpolation, to

know when we have sufficient accuracy in our interpolant.