If <span class="math-tex">\(\displaystyle\lim_{x\rightarrow \infty}\left(1+ \dfrac{a}{x}+\dfrac{b}{x^2}\right)^{2x}=e^2\)</span>, then the value of a and b are
This is a \(1^\infty\) form, so the limit = \(e^L\) with
\(L = \lim_{x \to \infty} 2x\left(\frac{a}{x} + \frac{b}{x^2}\right) = \lim_{x \to \infty}\left(2a + \frac{2b}{x}\right) = 2a\)
\(e^{2a} = e^2 \Rightarrow a = 1\). b has no effect, so it can be any real number.
Answer: (B) a = 1, b ∈ R
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