 Hi and welcome to our session. Let us discuss the following question. The question says evaluate the following limit and exercises 1 to 22. Limit x tends to 3, x to the power 4 minus 81 by 2x squared minus 5x minus 3. We know that limit of gx by hx as x tends to A is gA by hA. Now g of A is equal to 0 when there are two possible cases. One is g of A is also equal to 0. Now when g of A is also equal to 0, then limit of gx by hx as x tends to A takes the form of 0 by 0. In this case, we cancel the common factors from both numerator and denominator which vanishes at the limit point. The second case is if g of A is not equal to 0. Now in this case, limit of gx by hx as x tends to A takes the form of A by 0. We know that division by 0 is not defined. So in this case, limit does not exist. Let's now begin with the solution. The next question we have to evaluate limit x to the power 4 minus 81 by 2x squared minus 5x minus 3 as x tends to 3. Now this is of the form 0 by 0. So this means to evaluate the limit of this function, we have to first reduce it into lowest form. So this is equal to limit x tends to 3x to the power 4 minus 3 to the power 4 by On spreading the middle term, we get 2x squared minus 6x plus x minus 3. This is equal to limit x tends to 3. Now x to the power 4 can be written as square of x squared and 3 to the power 4 can be written as square of 3 squared upon 2x into x minus 3 plus 1 into x minus 3. And this is equal to limit x tends to 3x squared minus 3 squared into x squared plus 3 squared. We have used the identity of a squared minus b squared upon 2x plus 1 into x minus 3. Now this is equal to limit x tends to 3x plus 3 into x minus 3 into x squared plus 9 upon 2x plus 1 into x minus 3. Now cancel x minus 3 from both numerator and denominator. So we are left with limit x tends to 3x plus 3 into x squared plus 9 by 2x plus 1. We know that limit of gx by hx as x tends to a is g of a by hx. So using this limit of x plus 3 into x squared plus 9 upon 2x plus 1 as x tends to 3 is 3 plus 3 into 3 squared plus 9 by 2 into 3 plus 1. This is equal to 6 into 18 by 7 and this is equal to 108 by 7. Insta required limit is 108 by 7. This is our required answer. So this completes the session by intake care.