Problem $6\mathrm{.}1.(20$pts$)$ We have three ways to define the Euler number e $,$ as follow. $($a$)$ The number e is the number in the domain of the natural logarithm that satisfiesln e$=\_1^$e $(1)/($t$)$dt$=1($b$)$ e$=$lim$\_(\backslash$delta $->0)(1+\backslash$delta $)^((1)/(\backslash$delta $))=$lim$\_($n$->\backslash$infty $)(1+(1)/($n$))^($n$)($c$)$ e$=\_($n$=0)^(\backslash$infty $)(1)/($n$!)$ Is it possible to write codes to compute the number e based on the above definitions? Which definition provides the most efficient approach to approximate the number e $?$ In your answer, you should make sure the following: $($a$)$ You need to submit the codes and the corresponding result. $($b$)$ Your code for each should be based on an iterative algorithm. That is$,$ your code should consist of a loop procedure and usually it needs the result of n$-1$ or the result less than or equal to n$-1$ to obtain the result of n $.($c$)$ You may include the part to tell which code provides the most efficient approximation, in terms of the number of iterations or time. $($d$)$ In each of the iteration, you may need to specify the stopping criteria such as when you believe the precision is good enough and you should terminate the loop.