Question

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false. If $\lim _{x \rightarrow 0} f(x)=4$ and $\lim _{x \rightarrow 0} g(x)=0$, then $\lim _{x \rightarrow 0} f(x) g(x)=0$.

Name: Problem 90, Chapter 9: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-09-26T16:20:19-08:00
Duration: 2 min 33 s
Channel: William Semus
Description: Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false. If limx →0 f(x)=4 and limx →0 g(x)=0, then limx →0 f(x) g(x)=0.

   Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false.
If $\lim _{x \rightarrow 0} f(x)=4$ and $\lim _{x \rightarrow 0} g(x)=0$, then $\lim _{x \rightarrow 0} f(x) g(x)=0$.

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 9, Problem 90

Instant Answer

Solved by Expert William Semus

09/26/2021

Step 1

Explanation: According to the limit laws, the limit of a product is the product of the limits, provided that both limits exist. In this case, both limits exist: $\lim_{x \rightarrow 0} f(x) = 4$ and $\lim_{x \rightarrow 0} g(x) = 0$ So, we can find the limit Show more…

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Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false. If $\lim _{x \rightarrow 0} f(x)=4$ and $\lim _{x \rightarrow 0} g(x)=0$, then $\lim _{x \rightarrow 0} f(x) g(x)=0$.

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Key Concepts

Limit of a Function

This concept involves determining the value that a function f(x) approaches as x nears a particular point. In contexts like these, we are given that f(x) approaches 4 as x approaches 0, and g(x) approaches 0 as x approaches 0.

Limit Laws

Limit laws are a collection of rules that enable us to compute the limits of algebraic combinations of functions. The product rule, one of these laws, states that if the limits of f(x) and g(x) exist when x approaches a number, then the limit of the product f(x)g(x) is the product of the limits. Since lim f(x) = 4 and lim g(x) = 0, their product's limit is 4·0 = 0.

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