Discussion
\(\displaystyle\lim_{x \to 0} \frac{x\cos^{2}x}{\sin x}\) is equal to
Answer: E
The limit is 1.
\[ \begin{aligned} \lim_{x \to 0} \frac{x\cos^{2}x}{\sin x} &= \lim_{x \to 0} \frac{x}{\sin x} \cdot \cos^{2}x \\ &= 1 \times 1 \\ &= 1 \end{aligned} \]
0 would come from substituting \(x = 0\) in the numerator only, ignoring that the denominator also tends to 0, and 2 or 4 have no basis in the standard limit.
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