00:01
Hello, let's have a look on the question.
00:02
So, value of f of 1 is 2, f of 2 is 4 and f of 4 is equal to 16.
00:11
So we need to find out the value of f of 3.
00:14
So from here we can see that x0 is equal to 1, x1 is equal to 2 and x2 is equal to 4, y0 is equal to 2, y 1 is equal to 4 and y2 is equal to 16.
00:30
Using lagrange's interpolation method, we can use the formula f of x is equal to y -0, x minus x1, x -2, divided by x -0 minus x -1, x -0 -6 -2, plus y -1, x -1, plus y -1, x -1, x -9 -6 -2, plus y -1, x -1, x -1, x -1, x -2, divided by, y -1, x -1, x1 minus x0 x1 minus x2 plus y2 into x minus x0 x minus x1 divided by x2 minus x0 into x2 minus x1 so this will be equal to twice of x minus 2 x minus 4 divided by 1 minus 2 1 minus 4 plus y 1 is 4 this is x minus 1 into x minus 4 divided by 2 minus 1 into 2 minus 4 plus this value will be 16 into x minus 1 x minus 2 divided by 4 minus 1 4 minus 2 so this value will be equal to f of x is equal to 2 by 3 x minus 2 x minus 4 plus 2 x minus 1 x minus 4 plus 8 by 3 x minus 1 x minus 2 so now when they put the value of x this is equal to 2 by 3 into 3 minus 2 and 3 minus 4 minus 2 2 into 3 minus 1 into 3 minus 4 plus 8 by 3 minus 3 minus 3...