Question
Question 19 (5 points) saved Evaluate \( \lim _{x \rightarrow \infty} e^{x} \). If the corresponding limit is infinity, then insert INF in the blank. If the corresponding limit is negative infinity, then insert -INF in the blank. If the corresponding limit does not exist, then insert DNE in the blank. Otherwise, write the number as an integer or a reduced fraction.
Ask by Ross Rogers. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The limit is INF.
Solution
The limit you're evaluating is:
\[
\lim_{x \rightarrow \infty} e^{x}
\]
As \( x \) approaches infinity, the exponential function \( e^{x} \) grows without bound. Therefore:
\[
\lim_{x \rightarrow \infty} e^{x} = \infty
\]
According to the instructions provided:
- If the limit is infinity, insert **INF**.
**Answer:** INF
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
As \( x \) approaches infinity, \( e^x \) grows without bound, which means it increases exponentially. Thus, the limit evaluates to infinity. Therefore, you would insert INF in the blank.
