MCQ
$\mathop {\lim }\limits_{\theta \to {0^ + }} \,{\left( {\sin \theta } \right)^{\left( {\sin \theta - {{\sin }^2}\theta } \right)}}$ is
- ✓$1$
- B$e^{-1}$
- C${e^{ - 1/2}}$
- D$0$
✓
Answer
Correct option: A.
$1$
a
It is $0^{\circ}$ form
It is $0^{\circ}$ form
Let $\mathrm{y}=(\sin \theta)^{\left(\sin \theta-\sin ^{2} \theta\right)}$
$\ln y = (1 - \sin \theta )\left( {\sin \theta \ln \sin \theta } \right)$
$\ln y = \mathop {\lim }\limits_{\theta \to \infty } \frac{{\ln \sin \theta }}{{\cos {\mathop{\rm ec}\nolimits} \theta }}$ (Use $L'$ pital and solve)
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