 Hi, and welcome to the session. Let us discuss the following question. The question says, evaluate the following. Limits in exercises 1 to 22 limit x tends to 2, 3x squared minus x minus 10 by x squared minus 4. Before solving this question, we should know that if fx is a rational function, that means if fx is of the form gx by hx, well, gx and hx are polynomials such that gx, sorry, hx is not equal to 0, then limit of fx as x tends to a is equal to limit of gx by hx as x tends to a. Now by the algebra of limits, limit of quotient is equal to quotient of limits. So limit of gx by hx as x tends to a is equal to limit of gx as x tends to a upon limit of hx as x tends to a. We have learned that limit of the polynomial function is the value of the function at the prescribed point. So this means limit of gx as x tends to a is t of a, and limit of hx as x tends to a is h of a. Now h of a is equal to 0, then we have two possible cases. First possible case is that g of a is also equal to 0. Now if both h a and g of a is equal to 0, then limit takes the form 0 by 0. In this case, that means when g a by h a is of the form 0 by 0, we cancel the common factors from both numerator and denominator vanishes at the given limit point. Second possible case is when g of a is not equal to 0. In this case, limit takes the form a by 0, and we know that division by 0 is not defined. So in this case, we will say that limit does not exist. So keeping this in mind, let's now begin the distribution. In this question, we have to evaluate limit of 3x squared minus x minus 10 by x squared minus 4 as x tends to 2. Now this is a rational function, and we know that limit of gx by hx as x tends to a is g of a by h of a. On putting x as 2 in both numerator and denominator, we get 0 by 0. We have learned that if limit takes the form 0 by 0, then we have to first cancel the common factors from both numerator and denominator, which vanishes at the given limit point, that means 2 here. And then we will calculate the limit of the function. So let's now first reduce it into lowest form. On splitting the middle term in the numerator, we get 3x squared minus 6x plus 5 by x minus 10 by, we can write the denominator as x squared minus 2 squared. And this is equal to limit x tends to 2, 3x into x minus 2 plus 5 into x minus 2 by using identity of a squared minus b squared, x squared minus 2 squared is equal to x minus 2 into x plus 2. Now this is equal to limit x tends to 3x plus 5 into x minus 2 by x minus 2 into x plus 2. Now cancel x minus 2 from both numerator and denominator. So now we are left with limit x tends to 2, 3x plus 5 by x plus 2. Now this is equal to 3 into 2 plus 5 by 2 plus 2 because we know that limit of gx by hx as x tends to a is g of a by h of a when both ga and ha is not equal to 0. And this is equal to 11 by 4. Hence our required limit is 11 by 4. So this completes the session. Bye and take care.