JEE Mains · Maths · STD 11 - 12. limits
\(\lim \limits_{x \rightarrow 0} \frac{x\left(e^{\frac{\left(\sqrt{1+x^{2}+x^{4}}-1\right)}{x}}-1\right)}{\sqrt{1+x^{2}+x^{4}}-1}\) is equal to
- A does not exist.
- B \(\sqrt{ e }\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^{2}+x^{4}}-1\right) / x}-1\right)}{\sqrt{1+x^{2}+x^{4}}-1}\) \(\because \lim _{x \rightarrow 0} \frac{\sqrt{1+x^{2}+x^{4}}-1}{x}\left(\frac{0}{0}\right.\) from \()\)…
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