 Hello and how are you all today? My name is Priyanka and I should be helping you with the following question. Say evaluate limit x approaches to 0 fx where fx is equal to mod of x divided by x when x is not equal to 0 and 0 when x is equal to 0. Now before proceeding on we should be well aware that limit of a function exists if the left hand limit is equal to the right hand limit. This is the key idea towards this question. Now here in question we will be finding out the left hand limit of the function when x is equal to 0 and the right hand limit of the function when x is equal to 0. Here we have limit x approaches to 0 negative that is from the left hand side. Here the function will be mod of x over x since x is not equal to 0. So we have when x is less than 0 then mod of x is negative. So we have limit x approaches to 0 from the left hand side minus x over x which gives us the value as minus 1. Now here we have limit x approaches to 0 from the right hand side. Here the answer is mod of x over x. Now here when x is greater than 0 then mod of x is a positive value of x right. So therefore we have limit x approaches to 0 from the right hand side x over x that gives us the answer as 1. Now clearly limit x approaches to 0 from the right from the left hand side the function is not equal to the limit x approaches to 0 from the right hand side of the function. So limit does not exist to 0. Right this ends the solution hope you understood the concept well have a nice day ahead.