 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says which of the following functions are continuous at the indicated points and the ninth one is fx is equal to x if x is less than 0 and x is greater than or equal to 0 at x is equal to 0. Let us now begin with the solution and the given function fx is equal to x if x is less than 0, x is square if x is greater than or equal to 0 and we have to check continuity of f at x is equal to 0. So for that we will have to show that left hand limit is equal to right hand limit is equal to f0 where left hand limit is limit as h approaches to 0 from the left hand side f of a minus h where a is the point where we have to find the continuity and here a is equal to 0. So this can be written as limit as h approaches to 0 from the left hand side f of minus h. From the left hand side of 0 f of minus h is equal to minus h therefore we have limit as h approaches to 0 from the left hand side minus h which is equal to minus 0 or equal to 0. Now let us find the right hand limit which is equal to limit as h approaches to 0 from the right hand side f of a plus h here again a is equal to 0 so we have limit as h approaches to 0 from the positive side f of h and from the positive side its value is equal to x square so we have h square limit as h approaches to 0 from the right hand side which is equal to 0 square is equal to 0 and now let us find the value of the function the point 0 which is equal to 0 square is again equal to 0. Hence we have left hand limit is equal to the right hand limit is equal to f0 and thus we can say that fx is continuous 0 so our answer is continuous. That is completes the session hope you enjoyed the session take care and bye for now.