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

Short answer

(B) 3/2

Step-by-step solution

Identify the Relevant Function Definition

Since the question asks for the limit as x approaches 1 from the right (\(x \rightarrow 1 ^+ \)), examine the definition of f(x) for \(x > 1\), which is \(x/2 + 1\).

Substitute Limit Value

Next, substitute the value of x=1 into the function definition, so it becomes \(1/2 + 1 = 3/2\).

Conclude the Result

The value obtained is the limit of the function as \(x \rightarrow 1 ^+ \). Thus, \( \lim _ { x \rightarrow 1 } + f ( x ) = 3/2 \)