 Hi and how are you all today? My name is Priyanka and I shall be helping you with the following question. Please find limit x approaches to 5 fx where fx is equal to mod of x minus 5. Let us quickly proceed on with the solution. We will be finding the left hand limit of the function x is equal to 5 and also the right hand limit of the function x is equal to 5. Now here we have limit x approaches to 5 from the left hand side fx that is limit x approaches to 5 from the left hand side mod of x minus 5. Now when x is less than 5 we put the value of x as 5 minus h. So the value of mod of x will be equal to what? 5 minus h that is the positive 5 minus h. So we have limit h approaches to 0 5 minus h minus 5 which further gives us limit h approaches to 0 5 minus h minus 5 which on simplifying gives us the value as limit h approaches to 0 minus h which is further equal to 0. Now let us find out the right hand limit of the function also. We have limit x approaches to 5 from the right hand side function we have the function as mod of x minus 5. Now when x is greater than 5 we put the value of x as 5 plus h. So the value of mod of x will be 5 plus h itself. And now as x approaches to 5 from the right hand side h approaches to 0 so we have limit h approaches to 0 5 plus h minus 5 which on simplifying will give us the value as limit h approaches to 0 h which is further equal to 0. So clearly we can see that limit x approaches to 5 from the left hand side of the function is equal to limit x approaches to 5 from the right hand side and they both are equal to 0. So the answer to the session is 0. In the sense my session understood the concept well have a nice day.