Discussion
The value of \( \lim_{x \to 0} x \ln x \) is
Answer: C
The form is \( 0 \times (-\infty) \), so rewrite it as a quotient and differentiate:
\[ \lim_{x \to 0^{+}} \frac{\ln x}{1/x} \;=\; \lim_{x \to 0^{+}} \frac{1/x}{-1/x^{2}} \;=\; \lim_{x \to 0^{+}} (-x) \;=\; 0. \]
The logarithm diverges, but only as slowly as a logarithm, and the factor \( x \) goes to zero faster than it grows
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development