 Hello, and how are you all today? My name is Priyanka and I shall be helping you with the following question. Here, the question says, let a1, a2, till an be fixed real numbers and define a function fx is equal to x minus a1 into x minus a2 and so on till x minus an. What is limit x approaches to a1 fx? For some, a is not equal to a1, a2, till an and we need to compute the value of x approaches to a1 of fx. Sorry, x approaches to a fx. Now, to proceed on with this solution, first of all, we will consider the factor x minus a1. Now here, as x approaches to a1, x minus a1 will approach to exactly zero. So therefore, we can write that limit x approaches to a1, x minus a1 is equal to what? It is equal to zero. Now, considering the function which is given to us, here we are given the function as x minus a1 into x minus a2 and so on till x minus an. Now, using limits on both the sides, we have limit x approaches to a1 fx is equal to limit x approaches to a1, x minus a1, x minus a2 and so on till x minus an. Now, we have found out above that limit x approaches to a1, here, let us first, before using this condition that we have above, we can write the limit of this whole function as limit of x approaches to a1 and the function is x minus a1 into limit x approaches to a1, x minus a2 and so on till x minus an. Now, we have found out above that the value of this limit is equal to zero. So, zero into limit x approaches to a1 function x minus a2 and so on till x minus an. So, zero multiplied by anything will be equal to what? Exactly zero. So, we have limit x approaches to a1 fx value as zero. Now further, it is given to us that a is not equal to a1 a2 and so on till an. Now, therefore, we can say that considering the factor x minus a1 has x approaches to a1, x minus a1 approaches to a minus a1. Now here, we have substituted the value of x as a. So, we have limit x approaches to a, the value of fx equal to limit x approaches to a1, x minus a1, x minus a2 and so on till x minus an. Now here, we have its answer as equal to a minus a1 that is on using the limit that is x approaches to a. Now, in place of x, we have a over here. So, we have a minus a1, a minus a2 and so on till a minus a. So, we can write the answer as first of all the value of limit x approaches to a1 of the function which is given to us is equal to zero. And the value of limit x approaches to a of fx is found out above as a minus a1, a minus a2 and so on till a minus an. Right, so this concludes the answer. Hope you enjoyed and understood it too. Have a nice day ahead.