 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. Question says evaluate the following limits and exercises 1 to 22, limit of x plus 1 to the power 5 minus 1 by x as x tends to 0. Before solving this question we should first be well versed with theorem 2 given in your NCE article. The theorem 2 states that for any positive integer n, limit of x to the power n minus a to the power n upon x minus a as x tends to a is equal to n into a to the power n minus y. The knowledge of this theorem is the key idea in this question. Now put in with the solution in this question we have to evaluate limit of x plus 1 to the power 5 minus 1 by x as x tends to 0. In order to make use of this theorem we have to add and subtract 1 from the denominator. So on adding and subtracting 1 from the denominator we get limit x tends to 0 x plus 1 to the power 5 minus 1 upon x plus 1 minus 1. Now put y equals to x plus 1 so that y tends to 1 as x tends to 0. So now this is equal to limit y tends to 1 y to the power 5 minus 1 upon y minus 1. The key idea we know that limit x tends to a x to the power n minus a to the power n upon x minus a is equal to n into a to the power n minus 1. Now here in place of x we have 5, in place of n we have 5 and in place of a we have 1. So by using this theorem limit of y to the power 5 minus 1 upon y minus 1 as y tends to 1 is 5 into 1 to the power 5 minus 1 and this is equal to 5. Hence our required limit is 5. This completes the session. Hi and take care.