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)−h(x)

Accepted Answer

Welcome back, everyone assume that limit of A of X when X approaches four is equal to 10 limit of B of X. When X approaches four is equal to eight and limit of C of X. When X approaches four is equal to three, find the limit of the expression limit of A, of X divided by B of X minus C of X one, X approaches four. And we are given a four answer choices. A seven quotient limit law B 10 difference in product limit laws, C two quotient and difference limit laws and D five difference limit law, right? We essentially also want to state the limit law or laws applied in the solution. So let's analyze the given expression. We want to evaluate limit. When X approaches four of A of X divided by the difference between B of X and C of X. We want to recall that we can always distribute the limit for each function as long as those individual limits exist. So first of all, we are going to take the limit when X approaches four of A of X and then in the denominator, we're going to distribute the limit such that we're evaluating the difference between the limit when X approaches four of B FX and limit of C of X. When once again, X approaches four, if these three limits exist, then we can apply the quotient law, right? Because we have a ratio and the difference law because we have a difference within the denominator. First of all, we notice that in the numerator, we have a of X, right? This limit is 10 in the denominator. That's B of X minus C of X. So that's eight minus three. All of these limits exist individually, meaning we can apply those two laws and we end up with 10 divided by five which gives us two. If we look at the answer choices, that's option C two quotient and difference limit laws. 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)−h(x)

Key Concepts

Limit of a Function

Limit Laws

Algebraic Manipulation of Limits

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