If , then is…

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

If lim⁡x→−∞(3x4+2x2)sin⁡(1x)+∣x∣3+5∣x∣3+∣x∣2+∣x∣+1=k\lim_{x\to-\infty}\frac{(3x^4+2x^2)\sin\left(\frac{1}{x}\right)+|x|^3+5}{|x|^3+|x|^2+|x|+1}=k, then [k2]\left[\frac{k}{2}\right] is _____.

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