iran-konkur 2021 Q119

iran-konkur · Other · konkur-riazi_1400_specialized Sign Change & Interval Methods
119. If $\displaystyle\lim_{x \to -\infty} \frac{\sqrt[5\circ]{(a^2x^2-1)(a^4x^4-1)\cdots(a^{100}x^{100}-1)}}{a^{49}x^k - 1} = -1$, what are the values of $a$ and $k$?
(1) $k = 51,\ a = -1$ (2) $k = 51,\ a = 1$
(3) $k = 49,\ a = -1$ (4) $k = 49,\ a = 1$
\textbf{119.} If $\displaystyle\lim_{x \to -\infty} \frac{\sqrt[5\circ]{(a^2x^2-1)(a^4x^4-1)\cdots(a^{100}x^{100}-1)}}{a^{49}x^k - 1} = -1$, what are the values of $a$ and $k$?

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(1) $k = 51,\ a = -1$ \hfill (2) $k = 51,\ a = 1$

(3) $k = 49,\ a = -1$ \hfill (4) $k = 49,\ a = 1$

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