 Hello and how are you all today? The question says, find limit x approaches to 0 fx where fx is equal to x over mod of x when x is not equal to 0 and 0 when x is equal to 0. Now here we will be finding out the left hand limit of the function when the value of x is equal to 0 and the right hand limit of the function when the value of x is equal to 0. Now here we have limit x approaches to 0 from the left hand side fx as equal to, ahead fx will be x over mod of x. Now we know that when x is less than 0, then the value of mod of x is equal to minus x, isn't it? So we have limit x approaches to 0 from the right hand side x over minus x and that is the answer as minus 1. Now let us find out for the right hand limit also. We have limit x approaches to 0 from the right hand side fx, that is limit x approaches to 0 from right hand side x over mod of x. Now when x is greater than 0, then the value of mod of x is a positive x. So we have limit x approaches to 0 from the right hand side x over x which on simplifying gives us the value as 1. Now clearly limit x approaches to 0 from the left hand side is not equal to limit x approaches to 0 from the right hand side of the function. So we can say that limit does not exist had x is equal to 0 and this is the required answer to the solution. Hope you understood the concept well, have a very nice day ahead.