if-2x-a-x-lt-3-x-2-4-3-x-lt-2-x-2-ax-b-x-2-find-3a-b-

Question Number 147432 by mathdanisur last updated on 20/Jul/21

i f {\begin{cases} 2 x + a; x < - 3 \\ x^{2} - 4; - 3 ⩽ x < 2 \\ x^{2} + a x + b; x ⩾ 2 \end{cases}

f i n d 3 a - b = ?

Answered by liberty last updated on 21/Jul/21

(∙) \lim_{x \to - 3} f (x) = \lim_{x \to - 3} (2 x + a) = \lim_{x \to - 3} (x^{2} - 4)

\Rightarrow a - 6 = 5; a = 11

(∙) \lim_{x \to 2} (x^{2} - 4) = \lim_{x \to 2} (x^{2} + 11 x + b)

\Rightarrow 0 = 4 + 22 + b; b = - 26

\Leftrightarrow 3 a - b = 33 + 26 = 59

Commented by mathdanisur last updated on 21/Jul/21

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