Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compu...

Question

Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compute the following limits and state the limit laws used to justify your computations.

lim x→1 (f(x)−g(x))

Accepted Answer

Welcome back everyone. If limit of A of X, when X approaches four is equal to 12 and limit of B of X, when X approaches four is equal to eight, evaluate limit of A of X minus B of X. When X approaches four state, the limit law or laws applied in the solution, we given four answer choices. A says four difference limit law B says three difference and quotient limit laws C 20 quotient limit law and the seven constant multiple and quotient limit laws. So basically, if we look at the expression that we want to evaluate, we are evaluating the difference between two functions within our limit, right? So let's recall the difference limit law. Let's suppose that we have a limit when X approaches some number A and we are subtracting one function from the other. Let's suppose F of X minus G of X. As long as these two limits exist, we can rewrite this as a difference of two individual limits. So we are distributing the limit. So we get limit when X approaches A of F of X minus limit, when X approaches A of G of X and in this case, we can use that difference limit law or the two given functions. In our case, we are evaluating limit when X approaches four. So the number A is four and the difference is A of X minus B of X. As long as each individual limit exists, we can use the difference limit law and rewrite it as limit when X approaches four of A of X minus limit when X approaches four of B of X. And in our case limit, when X approaches four of A of X is 12 and limit of B of X when X approaches four is eight. So we are subtracting eight from 12 and this gives us four. So the correct answer to this problem would be a four difference limit law. Thank you for watching.

Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compute the following limits and state the limit laws used to justify your computations.

lim x→1 (f(x)−g(x))

Key Concepts

Limit of a Function

Limit Laws

Difference of Limits

Watch next