1、Differential in Linear Approximate Computation12Application of the differential in approximate computation000()()()()f xf xfxxx 1xexsin xx tan xx(1)1xx ln(1)xxThe local linearization for a given function is the fundamental idea in the approximate computation using the differential.0 xwe can approxim
2、ate the value of the function in a small neighborhood of .We list some useful first degree approximations as follows:By the approximate equality3Application of the differential in approximate computationFinish.1.0067 3.1.02 Find an approximation value forSolution:(1)1xx Since ,0.02x if we let13 and
3、,we have311.021(0.02)3Finish.31.51000 110003998.5.Find an approximation value forSolution:33998.510001.531.510 110009.995 110 10.001534Application of the differential in approximate computationFinish.0.03.e Find an approximation value forSolution:0.0310.030.97e.Find an approximation value forsin44.Because is a point in a small neighborhood of444180 4 000sinsincos()xxxxxSolution:and we havesin44sinsincos418044180 212180.0.6948
