Question

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Answer 1

Explicație pas cu pas:

y = mx + n

m = 2; n = -3

$m = \lim_{x \to \infty}\dfrac{f(x)}{x}$

$2 = \lim_{x \to \infty}\dfrac{a {x}^{2} + bx + 1}{2 {x}^{2} + 3x} = \dfrac{a}{2} \iff 2 = \dfrac{a}{2} \\ \implies \bf a = 4$

$n = \lim_{x \to \infty}(f(x) - mx)$

$- 3 = \lim_{x \to \infty} \bigg(\dfrac{4{x}^{2} + bx + 1}{2x + 3} - 2x \bigg) = \\ = \lim_{x \to \infty} \dfrac{4{x}^{2} + bx + 1 - 4 {x}^{2} - 6x}{2x + 3} \\ = \lim_{x \to \infty} \dfrac{(b - 6)x + 1}{2x + 3} = \dfrac{b - 6}{2}$

$- 3 = \dfrac{b - 6}{2} \iff b - 6 = - 6 \\ \implies \bf b = 0$

Answer 2

Răspuns:

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