MCQ
Evaluate the following limit :$ \displaystyle\lim_{\text{x} \rightarrow 0} \frac{\sin^2 3\text{x}}{\text{x}^2}$
- A1
- B3
- C9
- D0
Solution:
$ \displaystyle\lim_{\text{x} \rightarrow 0} \frac{\sin^2 3\text{x}}{\text{x}^2}$
$ =\displaystyle\lim_{\text{x} \rightarrow 0} \frac{\sin 3\text{x}}{\text{x}} \times\frac{\sin 3\text{x}}{\text{x}}$
$= \displaystyle\lim_{\text{x} \rightarrow 0} 3\Bigg(\frac{\sin 3\text{x}}{\text{3x}}\Bigg) \times3\Bigg(\frac{\sin 3\text{x}}{\text{3x}}\Bigg)$
$=3\displaystyle\lim_{\text{x} \rightarrow 0} \frac{\sin 3\text{x}}{\text{3x}}\times3\displaystyle\lim_{\text{x} \rightarrow 0} \frac{\sin 3\text{x}}{\text{3x}}$
$ = 3\times3=9$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
A plane is parallel to yz-plane so it is perpendicular to: