00:01
For this problem, we are given the function f of x equals the square root of sine inverse, also written as arc sign of x, the interval from 0 to 1, and the point a equals 1 over 2.
00:13
For the first part of the problem, we are asked to plot the function f over the given interval, which is the result shown here.
00:21
We are then asked to linearize or find a linearization for our function about the point given.
00:28
In this case, we have a equals 1 half.
00:31
So this is the linearization here shown in exact values.
00:36
Or if we want a decimal form, you can see that the linearization would be approximately 0 .37 plus 1 .19 times x minus 0 .5.
00:47
We are then asked to plot the function and its linearization over the interval shown here, where the blue line is the linearization and the orange is the original function.
00:55
And lastly, we are asked to plot the absolute error, rather, over the interval, and use that plot to estimate delta, such that x minus a less than delta implies that f of x minus l of x is less than epsilon.
01:13
For epsilon equals 0 .5, shown by that top orange line, 0 .1, shown by the green line, and 0 .01 .1.
01:26
To, or we can estimate then, based on the graph shown, that when epsilon equals 0 .5, it seems like we would want delta to be equal to about, well, let's see...