MCQ
$\operatorname{Lim}_{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}$ .................
- ✓$e$
- B$\frac{-2}{\mathrm{e}}$
- C$0$
- D$e-e^2$
$ =\operatorname{Lim}_{x \rightarrow 0}(-e) \frac{\left(e^{\frac{\ln (1+2 x)}{2 x}-1}-1\right)}{x} $
$ =\operatorname{Lim}_{x \rightarrow 0}(-e) \frac{\ln (1+2 x)-2 x}{2 x^2} $
$ =(-e) \times(-1) \frac{4}{2 \times 2}=e$
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વિધાન $-2:$ સમીકરણ $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ ના અંતરાલ $[0, \pi ]$ માં 2 ઉકેલો મળે