Find the limits in a), b), and c) below for the function \( f(x)=\frac{4 x}{x-7} \). Use \( -\infty \) and \( \infty \) when appropriate. a) Select the correct choice below and fill in any answer boxes in your choice. A. \( \lim _{x \rightarrow 7^{-}} f(x)=\square \) (Simplify your answer.) B. The limit does not exist and is neither \( -\infty \) nor \( \infty \).

As \( x \) approaches 7 from the left (denoted as \( 7^{-} \)), the function \( f(x)=\frac{4x}{x-7} \) behaves interestingly. The denominator \( x - 7 \) approaches zero but remains negative, while the numerator approaches \( 4 \cdot 7 = 28 \). Thus, you can find: \( \lim _{x \rightarrow 7^{-}} f(x) = \frac{28}{0^{-}} = -\infty. \) Now, let’s jump to the opposite side of 7! When approaching \( 7 \) from the right (denoted as \( 7^{+} \)), the denominator gets closer to zero but is positive. So, you can see: \( \lim _{x \rightarrow 7^{+}} f(x) = \frac{28}{0^{+}} = +\infty. \) So, the limits are negative infinity and positive infinity when coming from the left and right of 7, respectively!