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Question Number 185406 by greougoury555 last updated on 21/Jan/23

$$Ifa,b,canddareconstantssuchthat$$$$\underset{x\to 0}{\lim }\frac{{ax}^2+\sin bx+\sin cx+\sin dx}{3x^2+5x^4+7x^6}=8$$$$findthevalueofthesuma+b+c+d$$

Answered by witcher3 last updated on 21/Jan/23

$$\sim \underset{x\to 0}{\lim }\frac{{\mathrm{ax}}^2+(\mathrm{b}+\mathrm{c}+\mathrm{d})\mathrm{x}}{{3\mathrm{x}}^2}\Rightarrow \{\begin{array}{l}\mathrm{b}+\mathrm{c}+\mathrm{d}=0\\ \frac{\mathrm{a}}{3}=8\end{array}$$$$\iff (\mathrm{a}=24\mathrm{\&}\mathrm{b}+\mathrm{c}+\mathrm{d}=0$$$$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=24$$

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