00:01
Hello student, here we have an event that is f of x it is equal to cos x at a is equal to 0.
00:09
Now differentiating this function with respect to x we have f dash x it is equal to minus of sin x and differentiating again with respect to x we have f double dash x it is equal to minus of cos x.
00:24
Now here we have to find the value for f of x cos x at a equal to 0 the second order approximation function by f x by taylor polynomial it is given by the second order approximation approximation of a function f of x by taylor polynomial is given by that is f of it is given by the formula as that is f of x is approximately equal to f of a plus f dash a multiplied by x minus a plus 1 divided by 2 f double dash a that is multiplied by x minus a whole square here it is given a is equal to 0.
01:39
So, putting a equal to 0 we have f of x it is approximately equal to f of 0 plus f dash 0 and here x minus 0 that is x multiplied by x and plus of f double dash 0 that is f double dash 0 divided by 2 multiplied by x square.
02:00
Now we have a function f x f dash x and f double dash x.
02:04
So, putting x equal to 0 we have that is f of 0 it is equal to that is 1 and f dash 0 it is equal to 0 and f double dash 0 it is equal to minus 1.
02:19
Now putting the value from here we have for x is equal to 1 and a is equal to 0.
02:27
So, we have f of 1 this is equal to cos of 1 this is approximately equal to that is f of 0...