Limits and Continuity: Calculus 1 Homework Problems Part 4

In this live stream, We will start this lecture by reviewing laws for calculating limits and learning how to apply these laws. These laws are the main foundations that will help us compute all sorts of limits. Then, we will go over various examples to illustrate how to apply these laws. The examples chosen for this lecture are among the typical problems you will encounter in your homework assignments. To compute these limits we will use various algebraic techniques such as the factorization of polynomials and the rationalization of radicals using conjugate expressions. Then we will solve more than 25 homework problems on limits and continuity. Please do not forget to like the video and subscribe to our channel. Thanks! Suppose that the limit as x goes to b of f of x and the limit as x goes to b of g of x exists. The first limit law we review is the sum law. The limit as x goes to b of the sum f of x plus g of x is equal to the sum of limits. The second limit law is the difference law. The limit as x goes to b of the difference f of x minus g of x is equal to the difference of limits. The third limit law is the constant multiple law. The limit as x goes to b of the constant c times f of x is equal to c times the limit as x goes to b of f of x. The fourth limit law is the product law. The limit as x goes to b of the product f of x times g of x is equal to the product of limits. The fifth limit law is the quotient law. The limit as x goes to b of the quotient, f of x divided by g of x is equal to the quotient of limits. Provided that the limit as x goes to b of g of x is not zero. Now that we have reviewed the main limits laws, let us apply them in the following examples. In this first example, we are asked to compute the limit as h goes to 0 of the fraction 3 plus h square minus 9, divided by h. Looking at this function, we see that it is a rational function. Let us first replace h with 0 in the expression and see what we obtain. So when we replace h with 0, the expression becomes 3 plus 0 square minus 9, everything divided by 0.