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Question Number 199467 by Calculusboy last updated on 04/Nov/23

Answered by cortano12 last updated on 04/Nov/23

$$4=\underset{x\to \mathrm{\infty }}{\lim }\frac{(\mathrm{a}-2){\mathrm{x}}^3+(3+\mathrm{c}){\mathrm{x}}^2+(\mathrm{b}-3)\mathrm{x}+2+\mathrm{d}}{{\mathrm{x}}^2[\sqrt{1+\frac{\mathrm{a}}{\mathrm{x}}+\frac{3}{{\mathrm{x}}^2}+\frac{\mathrm{b}}{{\mathrm{x}}^3}+\frac{2}{{\mathrm{x}}^4}}+\sqrt{1+\frac{2}{\mathrm{x}}-\frac{\mathrm{c}}{{\mathrm{x}}^2}+\frac{3}{{\mathrm{x}}^3}-\frac{\mathrm{d}}{{\mathrm{x}}^4}}]}$$$$\{\begin{array}{l}\mathrm{a}-2=0\Rightarrow \mathrm{a}=2\\ \frac{3+\mathrm{c}}{2}=4\Rightarrow \mathrm{c}=5\\ \mathrm{b}-3=0\Rightarrow \mathrm{b}=3\\ 2+\mathrm{d}=0\Rightarrow \mathrm{d}=-2\end{array}$$

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