In class, we learned that the function ( ) 2 x x e e f x x = could be approximated by the function 2 4 ( ) 1 6 120 x x g x = + + , which is the first three terms of the Maclaurin series for f x( ) . Write a script that computes both the original form of f (x) and its approximation g x( ) at 10 p x = , where p =1,2,3,... . Starting at p = 1, repeatedly compute both f (x) and g x( ) with increasing values of p until either (10 ) p f or (10 )p g equals the exact value of 0 lim 2 x x x e e x . (You can compute the exact limit using LHpitals rule.) Precisely, the last value of p used should be the first value of p at which either (10 ) p f or (10 )p g equals the exact value of the limit, whichever comes first. Notice which function attains the exact value of the limit first! (You do no need to turn in this observation just observe for yourself.)

et - ex In class, we learned that the function f(x) = could be approximated by the function 2x g(x) =1+*+*, which is the first three terms of the Maclaurin series for f(x). Write a script 06 120 that computes both the original form of f(x) and its approximation g(x) at x = 10-P, where p=1,2,3,.... Starting at p=1, repeatedly compute both f(x) and g(x) with increasing values of et ex p until either f(10-P) or g(10-P) equals the exact value of lim e . (You can compute the **0 2x exact limit using L'Hpital's rule.) Precisely, the last value of p used should be the first value of p at which either f (10-P) or g(10-P) equals the exact value of the limit, whichever comes first. Notice which function attains the exact value of the limit first! (You do no need to turn in this observation - just observe for yourself.) Script Reset D MATLAB Documenta 1 format long e 3 % let f represent values of f(x) 4 % let g represent values of g(x) 5 % let p be the value used in the exponent in f(10^-p) and g(10^-p) 16 % final value of f 17 f 19 % final value of g 20 g 22 % first value of p at which one of f(10^-p) or g(10^-p) hits the exact value of the limit et - ex In class, we learned that the function f(x) = could be approximated by the function 2x g(x) =1+*+*, which is the first three terms of the Maclaurin series for f(x). Write a script 06 120 that computes both the original form of f(x) and its approximation g(x) at x = 10-P, where p=1,2,3,.... Starting at p=1, repeatedly compute both f(x) and g(x) with increasing values of et ex p until either f(10-P) or g(10-P) equals the exact value of lim e . (You can compute the **0 2x exact limit using L'Hpital's rule.) Precisely, the last value of p used should be the first value of p at which either f (10-P) or g(10-P) equals the exact value of the limit, whichever comes first. Notice which function attains the exact value of the limit first! (You do no need to turn in this observation - just observe for yourself.) Script Reset D MATLAB Documenta 1 format long e 3 % let f represent values of f(x) 4 % let g represent values of g(x) 5 % let p be the value used in the exponent in f(10^-p) and g(10^-p) 16 % final value of f 17 f 19 % final value of g 20 g 22 % first value of p at which one of f(10^-p) or g(10^-p) hits the exact value of the limit