00:01
So to find the intersection between the function fx and the gx, we first define the function out of x equal to the fx minus gx, option equal to the 2x plus 1 minus square root of the x plus 4.
00:21
So the 0 of arch x, obviously it is the intersection.
00:37
Of fx and gx.
00:43
So we need to find the zeros of the function of x and it will be the intersection of the fx and the gx.
00:50
So you need to find the zeros of the xx by newton's approach.
00:57
We need to find the arch prime of x will equal to the two minus.
01:03
So the so before we do the derivative to the h x let's try to continue to simplify the function x now this one will equal to the 2x plus 1 minus so i will turn this on to the power of the half and then the derivatives of the x will equal to so derivative to the 2x give us the 2 and the derivative of the 1 equal to 0 and now the next one will have the derivative of the power of the half so we should have minus we bring the half down and now inside we have x plus four power of minus a half now we times the derivative of the inside which is one so i simplify this one we should have this one equal to the two minus a half and now this one will be square root of the x plus four okay so also in a use the newton's approach we need to have the initial value which is x1 so let's say i let the x1 equal to 0 .5 and now by newton's approach my next x2 will equal to the x1 minus arch of the x1 divided by arch prime of x1 so this one will equal to so my x0 equal to so my x0 0 .5 minus my h x equal to 2 and now my x equals 0 .5 plus 1 minus 0 .5 plus 4 power a half.
02:59
And for the h prime x1 we have 2 minus 1 divide by 2 square root of the 0 .5 plus 4.
03:09
Plus 4.
03:11
So this one gives us equal to 0 .5 minus.
03:17
For the top, using the calculator, we should have 4 .5, square of 4 .5.
03:27
Let's answer, plus 1, plus 1.
03:33
So we go to minus 0 .1, 1, 2 ,000, and 3.
03:37
And from the denominator, we should have 2, minus 0 .1, 2, 1, 3 .3.
03:39
And from the denominator, we should have...