MCQ
The value of $\mathop {\lim }\limits_{x \to \infty } \sqrt {{a^2}{x^2} + ax + 1} - \sqrt {{a^2}{x^2} + 1} $ is
- ✓$\frac{1}{2}$
- B$1$
- C$2$
- DNone of these
$ = \mathop {\lim }\limits_{x \to \infty } \,\frac{{ax}}{{\,\sqrt {{a^2}{x^2} + ax + 1} + \sqrt {{a^2}{x^2} + 1} }}$
$ = \mathop {\lim }\limits_{x \to \infty } \,\frac{a}{{\,\sqrt {{a^2} + \frac{a}{x} + \frac{1}{{{x^2}}}} + \sqrt {{a^2} + \frac{1}{{{x^2}}}} }} = \frac{a}{{2a}} = \frac{1}{2}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Statement $1:$ If arg $Z+$ arg $W = \pi ,$ then $Z = -\overline W $.
Statement $2:$ $\left| Z \right| = \left| W \right|,$ implies arg $Z-$ arg $\overline W = \pi .$