Problem 3 . The goal of this problem is to show that the function f ( 2 ) 2 0 2 0 is infinitely differentiable , but not analytic .

Please help with this matlab code to compare with with I got

Problem 3 . The goal of this problem is to show that the functionf ( 2 )2 02 0is infinitely differentiable , but not analytic . Recall that a function of is analytic at- O if its MacLaurin series has positive radius of convergence and is equal f on theinterval of convergence( a ) Plot the function g ( 2 ) = e I using ezplot on the interval O , 10 get a feel for whatf looks like( 6 ) On a different plot , using ezplot again , plot g and its first 4 derivatives on the samegraph , over the interval O , 1( c ) Notice that it looks that gis O when a = ( well , has right hand limit equal to zero . )Let's verify this . After having declared a to be symbolic , the right hand limit of a g canbe computed aslimit ( 8 , x , limit value , right )Compute lim , 10 + 9 ( 2 ) . Explain in a comment why this makes f defined above contin -LOUS( 1 ) Since 9 is not defined at the origin , to check that g ( hence f ) is differentiable at Owe have to appeal to the limit definition of the derivative . We must check thatlim9 ( 0 + h ) - 9 ( 0)lim( 1 )hotnot hexists . What is it ?( e ) If you repeat this for the higher derivatives of g , you'll get the same answer asas In( 1 ) . Type in as a comment what the MacLaurin series of f ( x ) is , and conclude that fis not analytic