 Hi and welcome to our session. Let us discuss the following question. The question says evaluate the following limits in exercises 1 to 2. Limit of x to the power 10 plus x to the power 5 plus 1 by x minus 1 as x tends to minus 1. Before solving this question, we should know that if x is a rational function that means if x is of the power gx by hx well gx hx are polynomials such that gx is not equal to 0 then limit of 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 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. Now gx and hx are polynomial functions so limit of gx as x tends to a is g of a and limit of hx as x tends to a is h of a. The knowledge of this is a key idea in this question. Now beginning with the solution in this question we have to evaluate limit of x to the power 10 plus x to the power 5 plus 1 upon x minus 1 as x tends to minus 1. Now this function is of the form gx by hx and we know that limit of gx by hx as x tends to a is g of a upon h of a. So this means limit of this function is the value of this function at the point x equals to minus 1. So limit of x to the power 10 plus x to the power 5 plus 1 by x minus 1 as x tends to minus 1 is minus 1 to the power 10 plus minus 1 to the power 5 plus 1 upon minus 1 minus 1. This is equal to 1 minus 1 plus 1 by minus 2 and this is equal to minus 1 by 2. This required limit is minus 1 by 2. This is our required answer. So this can be an expectation i into a g.