If-a-b-c-and-d-are-constants-such-that-lim-x-0-ax-2-sin-bx-sin-cx-sin-dx-3x-2-5x-4-7x-6-8-find-the-value-of-the-sum-a-b-c-d-

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

I f a, b, c a n d d a r e c o n s t a n t s s u c h t h a t

\lim_{x \to 0} \frac{{a x}^{2} + \sin b x + \sin c x + \sin d x}{3 x^{2} + 5 x^{4} + 7 x^{6}} = 8

f i n d t h e v a l u e o f t h e s u m a + b + c + d

Answered by witcher3 last updated on 21/Jan/23

\sim \lim_{x \to 0} \frac{{ax}^{2} + (b + c + d) x}{{3 x}^{2}} \Rightarrow {\begin{cases} b + c + d = 0 \\ \frac{a}{3} = 8 \end{cases}

\Leftrightarrow (a = 24 & b + c + d = 0

a + b + c + d = 24

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