Question

Complete the tables and use the results to find the indicated limits. If $f(x)=2 x^{2}-4 x+7,$ find $\lim _{x \rightarrow 1} f(x)$ $$\begin{array}{|c|ccc}{x} & {0.9} & {0.99} & {0.999} & {1.001} & {1.01} & {1.1} \\ {f(x)} &&& {5.000002} & {5.000002}\end{array}$$

Name: Problem 16, Chapter 11: Finite Mathematics and Calculus with Applications
Uploaded: 2020-05-04T13:32:29-08:00
Duration: 3 min 8 s
Channel: Linh Vu
Description: Complete the tables and use the results to find the indicated limits. If f(x)=2 x^2-4 x+7, find limx →1 f(x) x 0.9 0.99 0.999 1.001 1.01 1.1 f(x) 5.000002 5.000002

   Complete the tables and use the results to find the indicated limits.
If $f(x)=2 x^{2}-4 x+7,$ find $\lim _{x \rightarrow 1} f(x)$
$$\begin{array}{|c|ccc}{x} & {0.9} & {0.99} & {0.999} & {1.001} & {1.01} & {1.1} \\ {f(x)} &&& {5.000002} & {5.000002}\end{array}$$

Finite Mathematics and Calculus with Applications

Margaret L. Lial,… 9th Edition

Chapter 11, Problem 16

Instant Answer

Solved by Expert Linh Vu

05/04/2020

Step 1

We can do this by substituting the given x-values into the function $f(x)=2 x^{2}-4 x+7$. Show more…

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Complete the tables and use the results to find the indicated limits. If $f(x)=2 x^{2}-4 x+7,$ find $\lim _{x \rightarrow 1} f(x)$ $$\begin{array}{|c|ccc}{x} & {0.9} & {0.99} & {0.999} & {1.001} & {1.01} & {1.1} \\ {f(x)} &&& {5.000002} & {5.000002}\end{array}$$

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Key Concepts

Limit of a Function

A limit describes the value that a function approaches as the input approaches a given number. In many cases, especially for continuous functions, the limit as x approaches a certain value is simply the value of the function at that point.

Continuity

Continuity refers to a function being uninterrupted or smooth at a point. A function is continuous at a point if its limit as x approaches that point equals the function’s actual value there. Polynomial functions are inherently continuous over all real numbers.

Direct Substitution Method

When a function is continuous at a specific point, the limit as x approaches that point can be found by directly substituting the value into the function. This simplifies the process of evaluating limits without the need for further manipulation.

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