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limit ((1 + 5x^2)(1/(x^2-3x)) (for x → 0) =.... |
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Answer» \(\lim\limits_{x \to 0} (1+5x^2)^{(\frac{1}{x^2-3x})}\) (1∞ type) = Exp{\(\lim\limits_{x \to 0} (1+5x^2-1)\times{\frac{1}{x^2-3x}}\)} = Exp{\(\lim\limits_{x \to 0} \frac{5x^2}{x^2-3x}\)} = Exp{\(\lim\limits_{x \to 0} \frac{5x}{x-3}\)} = Exp{\(\frac{5\times0}{0-3}\)} (By taking limit) = e0 = 1 ∴ \(\lim\limits_{x \to 0} (1+5x^2)^{\frac{1}{x^2-3x}}\) = 1 |
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