Asymptotic analysis

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Problem: Determine the order of smallness of \( \alpha(x)=\ln \left(x^{3}+3 x^{2}+3 x+2\right) \) with respect to \( \beta(x)=x+1 \) when \( x \rightarrow-1 \).

2.12.12 Asymptotic analysis

1 $

Problem: Determine the order of smallness of \( \alpha(x)=\sqrt{\cos \ln x}-1 \) with respect to \( \beta(x)=x-1 \) when \( x \rightarrow 1 \).

2.12.13 Asymptotic analysis

1.5 $

Problem: Find the leading term in the asymptotic expansion of the function: \[ F(\lambda)=\int_{-1}^{\infty} e^{-\lambda \sqrt{\frac{x^{2}}{1+x}}} d x \]

2.12.18 Asymptotic analysis

5.49 $

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