$\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^{2}+x^{4}}-1\right) / x}-1\right)}{\sqrt{1+x^{2}+x^{4}}-1}$
Correct Option: , 4
$\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^{2}+x^{4}}-1\right) / x}-1\right)}{\sqrt{1+x^{2}+x^{4}}-1}$
$\because \lim _{x \rightarrow 0} \frac{\sqrt{1+x^{2}+x^{4}}-1}{x}\left(\frac{0}{0}\right.$ from)
$\lim _{x \rightarrow 0} \frac{\left(1+x^{2}+x^{4}\right)-1}{x\left(\sqrt{1+x^{2}+x^{4}}+1\right.}$
$\lim _{x \rightarrow 0} \frac{x\left(1+x^{2}\right)}{\left(\sqrt{1+x^{2}+x^{4}}+1\right)}=0$
So $\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\frac{\sqrt{1+x^{2}+x^{4}}-1}{x}\right)}-1\right)}{\sqrt{1+x^{2}+x^{4}}-1}\left(\frac{0}{0}\right.$ from $)$
$\lim _{x \rightarrow 0} \frac{e^{\frac{\sqrt{1+x^{2}+x^{4}}-1}{x}}-1}{\left(\frac{\sqrt{1+x^{2}+x^{4}}-1}{x}\right)}=1$
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