29. Which of the following are true? $$ \begin{array}{llll} ext { I. } \lim _{x ightarrow \infty} \ln x^{2}=\infty & ext { II. } \lim _{x ightarrow 0} \ln x^{2}=-\infty & ext { III. } \lim _{x ightarrow-\infty} \ln x^{2}=\infty\end{array} $$ $$ \begin{array}{llll} ext { A. I only } & ext { B. II only } & ext { C. I and II } & ext { D. II and III }\end{array} $$ E. I, II, and III

Question

29. Which of the following are true? $$ \begin{array}{llll}	ext { I. } \lim _{x ightarrow \infty} \ln x^{2}=\infty & 	ext { II. } \lim _{x ightarrow 0} \ln x^{2}=-\infty & 	ext { III. } \lim _{x ightarrow-\infty} \ln x^{2}=\infty\end{array} $$ $$ \begin{array}{llll}	ext { A. I only } & 	ext { B. II only } & 	ext { C. I and II } & 	ext { D. II and III }\end{array} $$ E. I, II, and III

UpStudy AI · Accepted Answer

Let's evaluate each statement one by one:

**I.** $$\lim_{x \rightarrow \infty} \ln(x^2) = \infty$$

- As $$ x $$ approaches $$ \infty $$, $$ x^2 $$ also approaches $$ \infty $$.
- Therefore, $$ \ln(x^2) $$ approaches $$ \infty $$.
- **This statement is true.**

**II.** $$\lim_{x \rightarrow 0} \ln(x^2) = -\infty$$

- As $$ x $$ approaches $$ 0 $$, $$ x^2 $$ approaches $$ 0 $$ from the positive side.
- Therefore, $$ \ln(x^2) $$ approaches $$ \ln(0^+) $$, which is $$ -\infty $$.
- **This statement is true.**

**III.** $$\lim_{x \rightarrow -\infty} \ln(x^2) = \infty$$

- As $$ x $$ approaches $$ -\infty $$, $$ x^2 $$ approaches $$ \infty $$ (since squaring a negative number results in a positive number).
- Therefore, $$ \ln(x^2) $$ approaches $$ \infty $$.
- **This statement is true.**

Since all three statements are true, the correct answer is:

**E. I, II, and III**
All three statements are true: I, II, and III.

Which of the following are true?

E. I, II, and III

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Calculus Questions

Which of the following are true? E. I, II, and III