Please show full matlab script and run. $1-$ Using Taylor's series around

write a Matlab function that computes the function

with tolerance

$.$ You are not allowed to use exponentiation, trigonometric, factorials or transcendental functions $($will receive $0$ if you do so$).$ The function must be runnable when I copy and paste in Matlab $($look the example in this module, you will receive $0$ if it does not work$).$ Below the program, write the output of

with at least $10$ significant digits $($hint: the function should equal to the Matlab function besselj$(0,2*$x$)).$ Make sure your function does not output anything else than the final answer. You must show me the program running during office hours.

$2-$ Using Taylor series and double precision arithmetic, find what is the largest double precision number

such that

where

$.$ Verify your result in Matlab$\mathrm{.}1-$ Using Taylor's series around $x_0=0,$ write a Matlab function that computes the function

$f(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n{x}^{2n}}{(n!{)}^2}$

besselj $(0,2^{**}x)).$ Make sure your function does not output anything else than the final answer. You must show me the program running during office hours.

$2-$ Using Taylor series and double precision arithmetic, find what is the largest double precision number $x$ such that

$coshx=1$

where $coshx=\frac{e^x+e^{-x}}{2}.$ Verify your result in Matlab.