X- 0lim 1-2x-1-3x 1-x2-e1-x-

X→ 0lime^1/x^2(log(1+2x) log(1+3x))+1/x e^x→ 0lim(log(1+2x) log(1+3x))+x/x^2 Using the expansion we get =e^5/2 ...

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Expansions to Remove Indeterminate Form

x→ 0lim 1+2x/...

Question

$l i m x \to 0 {(\frac{1 + 2 x}{1 + 3 x})}^{\frac{1}{x^{2}}} . e^{\frac{1}{x}} =$

e^{\frac{5}{2}}

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e^{2}

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Solution

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