if-lim-x-a-3-x-3-4x-2-cx-4-bx-2-9x-7-1-2-find-a-b-

Question Number 145851 by mathdanisur last updated on 08/Jul/21

i f \underset{x \to \infty}{l i m} \frac{(a - 3) x^{3} + 4 x^{2} + c x + 4}{{b x}^{2} + 9 x + 7} = \frac{1}{2}

f i n d a + b = ?

Answered by Olaf_Thorendsen last updated on 08/Jul/21

a - 3 = 0 \Rightarrow a = 3

\frac{4}{b} = \frac{1}{2} \Rightarrow b = 8

a + b = 11

Commented by mathdanisur last updated on 09/Jul/21

t h s n k s S e r

Answered by mathmax by abdo last updated on 09/Jul/21

\Rightarrow \lim_{x \to + \infty} \frac{2 (a - 3) x^{3} + {8 x}^{2} + 2 cx + 8}{{bx}^{2} + 9 x + 7} = 1 \Rightarrow

{\begin{cases} a - 3 = 0 \\ b = 8 \Rightarrow {\begin{cases} a = 3 \\ b = 8 \Rightarrow a + b = 11 \end{cases} \end{cases}

Commented by mathdanisur last updated on 09/Jul/21

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