QuestionFind $\lim _{x \rightarrow 2^{+}} f(x)$ for the piecewise function: $f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a piecewise function defined as - $f(x) =5x -3$ for $x <$ - $f(x) =9$ for $x =$ - $f(x) =4x +3$ for $x >$ . We are asked to find the limit of $f(x)$ as $x$ approaches from the right, denoted as $\lim{x \rightarrow^{+}} f(x)$

STEP 2

The limit as $x$ approaches2 from the right, $\lim{x \rightarrow2^{+}} f(x)$ , refers to the value that $f(x)$ approaches as $x$ gets infinitely close to2, but is still greater than2.

STEP 3

Since $x$ is greater than2, we should use the part of the piecewise function defined for $x >2$ , which is $f(x) =x +3$ .

STEP 4

Substitute $x =2$ into the function $f(x) =4x +3$ .
$f(2) =4(2) +3$

STEP 5

Calculate the value of $f(2)$ .
$f(2) =4(2) +3 =8 +3 =11$ So, $\lim{x \rightarrow2^{+}} f(x) =11$ .
The correct answer is (C)11.

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