In Exercises 67 - 70 , use the following function. f ( x ) = { 2 - x , x ≤ 1 ( x )

Name: Problem 68, Chapter 2: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2019-05-15T05:39:39-08:00
Duration: 1 min 26 s
Channel: Sooyeon Kim
Description: In Exercises 67 - 70 , use the following function. f ( x ) = { 2 - x , x ≤ 1 ( x )/( 2 ) + 1 , x > 1 . Multiple Choice What is the value of lim x →1 + f ( x ) ? (A) 5/ 2 ( B ) 3 / 2 ( 𝐂 ) 1 ( 𝐃 ) 0 (E) does not exist

step 1 Question 68 asks, what is the value of limit of F of X as X approaches one from the right side?

Question

In Exercises $67 - 70$ , use the following function. $f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$ Multiple Choice What is the value of $\lim _ { x \rightarrow 1 } + f ( x ) ?$ (A) 5$/ 2$ $( \mathrm { B } ) 3 / 2$ $( \mathbf { C } ) 1$ $( \mathbf { D } ) 0$ (E) does not exist

   In Exercises $67 - 70$ , use the following function.

$f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$

Multiple Choice What is the value of $\lim _ { x \rightarrow 1 } + f ( x ) ?$

(A) 5$/ 2$ $( \mathrm { B } ) 3 / 2$ $( \mathbf { C } ) 1$ $( \mathbf { D } ) 0$  (E) does not exist

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 3rd Edition

Chapter 2, Problem 68

Instant Answer

Solved by Expert Sooyeon Kim

05/15/2019

Step 1

This is denoted as $\lim _ { x \rightarrow 1^+ } f ( x )$. Show more…

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In Exercises $67 - 70$ , use the following function. $f ( x ) = \left\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.$ Multiple Choice What is the value of $\lim _ { x \rightarrow 1 } + f ( x ) ?$ (A) 5$/ 2$ $( \mathrm { B } ) 3 / 2$ $( \mathbf { C } ) 1$ $( \mathbf { D } ) 0$ (E) does not exist

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Key Concepts

Limit Evaluation at a Point

Limit evaluation at a point means determining the value that a function approaches as the input approaches a specific value. When the function is defined differently on different intervals, evaluating the left-hand limit and right-hand limit separately is essential to understand the function’s behavior near that point.

Piecewise-Defined Functions

A piecewise-defined function is one that has different expressions for different parts of its domain. Understanding these functions involves determining which formula applies for a given input value based on conditions defined for the function's intervals.

One-Sided Limits

One-sided limits involve evaluating the behavior of a function as the independent variable approaches a particular point from one side (either from the left or from the right). This concept is crucial when dealing with piecewise functions, because the function may have different behaviors on either side of a boundary point.

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