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$f(x) = 72 \ln(x)$ for $x < 0$ for $\infty > 0$ Find $\lim_{x \to +1} f(x)$ . Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $1$ $\newline$ (C) $e$ $\newline$ (D) The limit doesn't exist.

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Determine end behavior of polynomial and rational functions

Full solution

Q.

f(x) = 72 \ln(x)

for

x < 0

for

\infty > 0

Find

\lim_{x \to +1} f(x)

. Choose

1

answer:

\newline

(A)

0

\newline

(B)

1

\newline

(C)

e

\newline

(D) The limit doesn't exist.

Understand given function: First, we need to understand the function given. The function $f(x) = 72 \ln(x)$ is only defined for $x < 0$ , and it's $\infty$ for $x > 0$ . We're looking for the limit as $x$ approaches $1$ from the left, which means we're interested in the behavior of the function just before $x$ reaches $1$ .
Approaching $1$ from left: Since we're approaching $1$ from the left, we're actually looking at values of $x$ that are less than $1$ . However, the function $f(x) = 72 \ln(x)$ is not defined for $x \geq 0$ , so we can't use this part of the function to find the limit as $x$ approaches $1$ from the left.
Function behavior near boundary: The other part of the function says that $f(x)$ is $\infty$ for $x > 0$ . As we approach $1$ from the left, we're getting closer to the boundary where the function switches to $\infty$ . But since we never actually reach $x > 0$ from the left side, we can't say the limit is $\infty$ .
Limit does not exist: Therefore, since the function is not defined for $x \geq 0$ , and we're approaching $1$ from the left, the limit does not exist because there's no value of $f(x)$ that $x$ can approach as it gets close to $1$ from the left side.

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