 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question says, find the values of k so that the function f is continuous at indicated point. fx is equal to kx plus 1 if x is less than equal to pi. fx is equal to cos x if x is greater than pi. fx is equal to pi at x is equal to pi. First of all let us understand that if function f is continuous at x is equal to a, then left hand side limit of the function is equal to right hand side limit of the function is equal to value of the function at x is equal to a. Or we can say limit of x tending to a minus fx is equal to limit of x tending to a plus fx is equal to fa. This is the left hand side limit of the function. This is right hand side limit of the function and this is the value of the function at x is equal to a. This is the key idea to solve the given question. Let us now start the solution. We are given fx is equal to kx plus 1 if x is less than equal to pi and fx is equal to cos x if x is greater than pi. Also we are given function f is continuous at x is equal to pi. First of all let us find out left hand side limit of the function at x is equal to pi. So we can write limit of x tending to i minus fx is equal to limit of x tending to i minus kx plus 1 is equal to i k plus 1. So we get limit of x tending to pi minus fx is equal to pi k plus 1. Now let us find out right hand side limit of the function at x is equal to pi. So we can write limit of x tending to pi plus fx is equal to limit of x tending to pi plus cos x. This is equal to cos pi which is equal to minus 1. So we get limit of x tending to pi plus fx is equal to minus 1. We know cos pi is equal to minus 1. So we get right hand side limit of the function at x is equal to pi as minus 1. Now we know that given function is continuous. So left hand side limit and right hand side limit of the function at x is equal to pi must be equal. Now substituting the corresponding values of the limits we get pi k plus 1 is equal to minus 1. This implies pi k is equal to minus 1 minus 1. This implies pi k is equal to minus 2. This implies k is equal to minus 2 upon pi. So required value of k is equal to minus 2 upon pi. This is our required answer. This completes the session. Hope you understood the session. Goodbye.