 Hi and welcome to the session. Let us discuss the following question. Question says, prove that the function fx is equal to x raised to the power n is continuous at x is equal to n, where n is a positive integer. First of all let us understand that function f is continuous at x is equal to a if function is defined at x is equal to a or we can say f a exist. Limit of the function is equal to 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 know function f is given by fx is equal to x raised to the power n, where n is any positive integer. Now we have to find if the given function is continuous at x is equal to n, where n is a positive integer. Now clearly we can see at any positive integer n given function is defined. So we can write function f is defined at x is equal to n where n is any positive integer. Now let us find out limit of the function at x is equal to n. So we can write limit of x tending to n fx is equal to limit of x tending to n x raised to the power n, which is further equal to n raised to the power n, where n is any positive integer. Now let us find out value of the function at x is equal to n. That is we will find out fn which is equal to n raised to the power n, where n belongs to positive integers. Now clearly we can see limit of the function is equal to value of the function at x is equal to a. So we can write limit of x tending to n fx is equal to fn is equal to n raised to the power n. This implies function f is continuous at x is equal to n. So here we have proved that function f is continuous at x is equal to n, where n is any positive integer. This is our required answer. This completes the session. Hope you understood the session. Take care and keep smiling.