Homework Sourse2 Let gx cos x 1 x 2 2 Use a calculator to compute the av
(2) Let g(x) =
cos x 1
x
2 + 2
. Use a calculator to compute the average ROC of on the intervals [:1; 0],
[:01; 0]; [:001; 0]; [:0001; 0]; [0; :1]; [0; :01]; [0; :001], and [0; :0001]. Record the values to at least
four decimal places. Use that data to guess the instantaneous ROC of g at x = 0. Be sure your
calculator is set in radian mode. (Degrees are rarely used in calculus, so leave your calculator in
radian mode.)
cos x 1
x
2 + 2
. Use a calculator to compute the average ROC of on the intervals [:1; 0],
[:01; 0]; [:001; 0]; [:0001; 0]; [0; :1]; [0; :01]; [0; :001], and [0; :0001]. Record the values to at least
four decimal places. Use that data to guess the instantaneous ROC of g at x = 0. Be sure your
calculator is set in radian mode. (Degrees are rarely used in calculus, so leave your calculator in
radian mode.)
Solution
Cosine normally runs between -1 and 1. By subtracting 1 from it, you have changed its range to -2 to 0. So its absolute value runs from 0 to 2. So work this backwards -- you want the point where: |cos(x) - 1| = 2 cos(x) - 1 = -2 cos(x) = -1 which is x = p (straight left on the unit circle).![(2) Let g(x) = cos x 1 x 2 + 2 . Use a calculator to compute the average ROC of on the intervals [:1; 0], [:01; 0]; [:001; 0]; [:0001; 0]; [0; :1]; [0; :01]; [0](/WebImages/35/2-let-gx-cos-x-1-x-2-2-use-a-calculator-to-compute-the-av-1103246-1761583382-0.webp "(2) Let g(x) = cos x 1 x 2 + 2 . Use a calculator to compute the average ROC of on the intervals [:1; 0], [:01; 0]; [:001; 0]; [:0001; 0]; [0; :1]; [0; :01]; [0")
