Question

f(x) = \

$$\begin{cases} x^2 - 4x + 4 & \\text{for } x < 2 \\\\ 3 & \\text{for } x = 2 \\\\ x^2 - 4x + 8 & \\text{for } x > 2 \\end{cases}$$

let $f$ be the piecewise function defined above. the value of $\lim\limits_{x \to 2^+} f(x)$ is
\

$$\begin{enumerate}a \\item 0 \\item 3 \\item 4 \\item nonexistent \\end{enumerate}$$

Explanation:

Step1: Identify the right-hand limit function

For \( \lim_{x \to 2^+} f(x) \), we use the piece of the function where \( x > 2 \), which is \( f(x)=x^2 - 4x + 8 \).

Step2: Substitute \( x = 2 \) into the function

Substitute \( x = 2 \) into \( x^2 - 4x + 8 \):
\( (2)^2 - 4(2) + 8 = 4 - 8 + 8 \)

Step3: Simplify the expression

Simplify \( 4 - 8 + 8 \):
\( 4 - 8 + 8 = 4 \)

Answer:

C. 4