$1.$Write a function by using sagemath to find

a$)$ the dot product of two input vectors with same length $($Name this function "Dot"$),$

b$)$use "Dot" function to find the norm of the vector $(3,4)$ in R$^2.$

$2.$Write a sympy program to determine whether the function $1/$x is continous or not at a given real number a$.$

$3.$Write a sympy program to find the global maximum and minimum of x$^5+30$x$^3+50$x on the interval $[-5,5]$

$4.$a$)$In python, using sympy create the expression f$($x$)=$sin$($x$)$e$^-$x$,$

b$)$Integrate the function f$($x$).$ Then differenttiate the result to see if you get back the original function.