If limx - 0 1 - a3 - 8e1-x1 - 1 - b3e1-x - 2 - then

e ^ 1 x #160; at(x=0)=∞ lim _ x→ 0 (1+ a ^ 3 )+8 e ^ 1 x #160; 1+(1 b ^ 3 ) e ^ 1 x #160; #160; lim _ x→ 0 e ^ 1 x #160; ...

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Higher Order Derivatives

If limx → 0...

Question

If $lim x \to 0 \frac{(1 + a^{3}) + 8 e^{1 / x}}{1 + (1 - b^{3}) e^{1 / x}} = 2$ , then

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Solution

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lim x \to 0 \frac{(1 + a^{3}) + 8 e^{1 / x}}{1 + (1 - b^{3}) e^{1 / x}} = 2

lim x \to 0 \frac{(1 + a^{3}) + 8 e^{\frac{1}{x}}}{1 + (2 + b + b^{2}) e^{\frac{1}{x}}} = 2

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$lim x \to 0 \frac{(1 + x)^{\frac{1}{2}} - (1 - x)^{\frac{1}{2}}}{x}$

\lim_{x \to 0} \frac{\sqrt{1 + x^{2}} - \sqrt{1 + x}}{\sqrt{1 + x^{3}} - \sqrt{1 + x}}

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