$\lim_{x \rightarrow 0} \frac{x \left( e^{\frac{\sqrt{1+x^{2}+x^{4}}-1}{x}} - 1 \right)}{\sqrt{1+x^{2}+x^{4}}-1}$ का मान ज्ञात कीजिए।
- Aअस्तित्व में नहीं है।
- B$\sqrt{e}$
- C$0$
- D$1$
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जब $n$ एक पूर्णांक है,तो $\mathop {Lim}\limits_{n \to \infty } \cos \left( {\pi \sqrt {{n^2} + n} } \right)$ का मान ज्ञात कीजिए:
$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^{1/x}} - e + \frac{1}{2}ex}}{{{x^2}}}$ का मान ज्ञात कीजिए।
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View Solution$\lim _{n}$ ${\rightarrow \infty} n^{-n k} \left\{(n+1)\left(n+\frac{1}{2}\right)\left(n+\frac{1}{2^2}\right) \ldots\left(n+\frac{1}{2^{k-1}}\right)\right\}^n=$
$\lim _{x \rightarrow 0} \frac{6^x-3^x-2^x+1}{x^2}$ का मान ज्ञात कीजिए।
यदि $\alpha=\lim _{x \rightarrow 0} \frac{x \cdot 2^x-x}{1-\cos x}$ और $\beta=\lim _{x \rightarrow 0} \frac{x \cdot 2^x-x}{\sqrt{1+x^2}-\sqrt{1-x^2}}$ है,तो
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